Of course we now know that bubonic plague is spread by fleas on rats that jump onto and bite humans, and that it is rarely if ever spread from person to person (unless I am mistaken about this?)

You are indeed mistaken. Bubonic Plague does spread from person to person, but it has to infect a person's lungs for it to do that - a variation called Pneumonic Plague. Here's an adaptation from an old answer explaining how the disease (more specifically it was about the Black Death) actually works:

The disease is yersinia pestis. Yersinia pestis is a bacteria which can infect a person in three ways: bubonic, pneumonic, and septicaemic.

Bubonic Plague spread through the bite of fleas. Through the skin, yersinia pestis binds itself to white blood cells until it infects the lymph nodes, which are little organs which produce white blood cells and antibodies. Once there, the bacteria is surrounded by the chemicals it needs to survive and reproduce quickly. As a result, the lymph nodes swell up which is where the distinctive buboes come from. The infection will then spread throughout the lymphatic system, damaging blood vessels which may cause gangrene as well as the coughing, excreting, and vomiting of blood. yersinia pestis binds to chemicals used by the lymphatic system to communicate, so not only is the body deprived of the organs used to produce white blood cells, but it doesn't know where to send the white blood cells it does have. Once the body realises that the infection cannot be stopped in this way, it will progress to sepsis. If the antibodies of white blood cells are a precision missile, then sepsis is carpet bombing, and the last resort of the immune system. It will throw everything at the disease, and damage organs and blood vessels in the process. This is especially bad with an infection of yersinia pestis because the blood vessels have already been damaged and the immune system is effectively blind, so it doesn't know where to direct all its bacteria-destroying cells. The victim suffers catastrophic organ failure and dies.

Septicaemic Plague is when yersinia pestis manages to reproduce in blood vessels without having to settle in a lymph node. It causes serious damage to blood vessels and leaches iron from red blood cells, resulting in cell death, serious blood loss from infected areas, and eventual organ failure. Septicaemic Plague is almost always a result of first contracting another form of plague, such as if Bubonic Plague got stuck in a blood vessel and began reproducing there. Septicaemic Plague acts as a pathway to the two other plagues, as bacteria in the blood can become dislodged and settle in the lungs and/or lymph nodes. On it's own though, it will directly cause organ failure by killing red blood cells, effectively suffocating the body from within, or by triggering sepsis. It has a 100% mortality rate.

Pneumonic Plague is yersinia pestis in the lungs. This is the most dangerous form of plague because it can be spread by droplets (mainly sneezing) and doesn't need fleas to infect others. In the lungs, yersinia pestis directly attacks the respiratory system. The victim will suffer breathing problems and eventually suffocate, though the infection may trigger sepsis before then. This form has a ~95% mortality rate and can kill in 36 hours. Even today, if it isn't treated within 24 hours of symptoms showing, the victim will almost certainly die an agonising death.

Although the beuboes were the most obvious sign of infection, those who became familiar with treating the disease knew that the pneumonic infection was the main killer. As Flemmish monk (monks often had the unfortunate job of treating and burying victims) Lodewijk Heyligen noted during the Black Death:

It is said that the plague takes three forms. In the first people suffer an infection of the lungs, which leads to breathing difficulties. Whoever has this corruption or contamination to any extent cannot escape but will die within two days. [the other two forms are both Bubonic Plague]

So it could easily spread person to person in a crowded city. When your author writes about 'breathing death upon them', that is not metaphor... People at the time knew that simply chatting with an afflicted person was enough to catch it, even if they did not understand why. As Giovanni Boccaccio, who was stuck in Florence during the Black Death, explained in his introduction to The Decameron:

Moreover, the virulence of the pest was the greater by reason the intercourse was apt to convey it from the sick to the whole, just as fire devours things dry or greasy when they are brought close to it, the evil went yet further, for not merely by speech or association with the sick was the malady communicated to the healthy with consequent peril of common death; but any that touched the clothes the sick or aught else that had been touched, or used by these seemed thereby to contract the disease.

The passage you quote is essentially the result of the above; that the plague could spread person to person; that normal things like talking, kissing, hugging etc. could easily kill loved ones. Those who walked around trying to help could easily become carriers themselves.

So even centuries before the outbreaks you're asking about, people knew that plague spread person to person, and actually considered this the primary cause. They had no real knowledge of why, but it was impossible to avoid the obvious contagiousness of the disease. Quarantines were a direct response to this understanding. The miasmic theory of disease was certainly popular (Giovanni does record some people wandering around Florence carrying freshly picked flowers to ward off plague) but they were smart enough to realise that air freshener could not defeat plague, they just thought it improved one's odds a little. They knew that the best way to not get sick was to avoid other sick people, though they attributed it to the air around them rather than the stuff in that air.

Elaborating a bit on the excellent response of u/J-Force, I would like to note that the importance of 'germ theory' that is often mentioned in such a context, is often misconstrued. The most important element of the latter was the discovery and isolation of the actual pathogens (initially the bacteria) that allowed proper targeting of the cause of various illnesses. But even before that discovery, people were perfectly aware that the medical condition can be transferred from person to person upon contact or even by being present in the general vicinity of the diseased person. This allowed people in pre-modern times to apply various effective preventive measures, even though the ability to consciously treat the condition was still beyond their capability. I'm using the term 'consciously', because it was possible to abate the infection to the point it became manageable by the immune system via incidental administration of natural antibiotics.

Furthermore, the term 'germ theory' is based on the concept used in 2nd century by Galen in his treatise De symptomatum causis and commentaries to Hippocrates' De morbis vulgaribus, where he suggests that diseases might be caused by an agent that can be transmitted and affect various people and also be transmitted from person to person. Technical inability to research microbiology led to the emergence of the miasma theory that usually made a connection with Galen's ideas to an easily discernible factors, such as rotten organic matter or other form of filth. But the idea was there. It is especially well visible in the case of the leprosy, under which was most likely a catch-all term people in Middle Ages applied to all conditions causing severe skin lesions and disfigurement. Treatment of lepers allows an assumption that the idea of sequestering the diseased and limiting contact with items they were using (already mentioned in Bible) was very well known and widely practiced.

For example, Bartholomeus Anglicus, drawing upon Constantinus Africanus and Al-Zahrawi has noted in his Liber de proprietatibus rerum published in 1247 that 'leprosy comes of diverse causes besides the aforementioned humours [...] for the evil is contagious and infects other men'. He also mentions that it possible to contract the leprosy via sexual contact, especially with prostitutes, as 'their wombs can still retain the semen of leprous clients' as well as it is possible for a wet nurse to infect the child during feeding. Although the author's explanation is not itself correct from medical standpoint, it might have been based on the proper observations that the leprosy and other skin conditions can be transferred by direct physical contact and, more importantly, is a testament to the fact that people were aware of the fact that the contact, including sexual one may be a vector of disease transmission.

It is sometimes posited that the general isolation of the lepers was caused by the religious reasons as the disease was considered a divine punishment for a sinful life and thus lepers were treated more like impious rather than sick. This, however, is often criticized as the moralistic stance quite prevalent in late 19th century, especially in Victorian England, that does not correspond to the historical and archaeological evidence. There are ecclesiastical accounts stating that leprosy was explained as the example of 'living through the purgatory on Earth' (with social separation and shunning being a part of purifying torment) and as Church was pretty clear on that with the exception of saints, everyone is destined to spend some time in that place, lepers were essentially no bigger sinners than most of the people. Touati and Rawcliffe note that this could have been largely caused by the fact that lepers, being unable to lead a normal social life were often turning to spiritual life and sequestering themselves not unlike anchorite saints whose endeavors were a common trope in Church's teachings. And indeed, the congregations of the lepers, already present in 12th century both in Europe and Holy Land, were operating not unlike monastic institutions and lay communes.

Furthermore, graves located in the vicinity of English leprosaria, like the hospital of St Mary Magdalene in Chichester that likely contain the remains of lepers rarely intercut, meaning that they were dug separately and were most likely marked. Burial in a marked grave on sanctified ground was definitely not the norm for social outcasts, especially those who were shunned on religious grounds. It should also be mentioned that Canon XXIII of the Third Lateran Council of 1179 states that no one can oppose the lepers who live together to have their separate churches, priests and graveyards, as they are forbidden to visit churches where the healthy people congregate. The same canon also mention that such churches should enjoy the relief from the tenth, customarily collected from ecclesiastical land. Such provisions show that in the eyes of the 12th century Church lepers were sick that should be cared for rather than the outcasts to be reviled. Rawcliffe also posits that the stereotypical image of a leper announcing his presence with a bell or a clapper is a result of the regulations applied to the transient lepers who, having been mobile and unknown in the given area, could have posed a higher epidemiological threat than the known, local lepers.

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Kinzelbach, A., Infection, Contagion, and Public Health in Late Medieval and Early Modern German Imperial Towns, in: Journal of the History of Medicine and Allied Sciences 61, no. 3, pp. 369-389.

Rawcliffe, C., Leprosy in Medieval England. Woodbridge, Boydell Press, 2006.

Touati, F.-O., Maladie et societe au moyen age. La lepre, les lepreux et les leproseries dans la province ecclesiastique de Sens jusqu'au millieu de XIVe siecle [Sickness and the society in the Middle Ages. Leprosy, lepers and leprosaries in the ecclesiastical province of Sens in the mid-14th century]. Paris, 1998.