I don't think anyone can say whether a nickname like that is really "deserved". Trying to answer that directly is almost definitely going to lead people into whataboutism and suchlike, so I'm just going to focus on your primary question and then contextualize it.
As far as I'm aware, the number of Marian martyrs that we have is really taken from John Foxe's Actes and Monuments, a Protestant polemic published in 1563; in its Book of Martyrs, it lists 312 people who were arrested for their religion and either burned to death or allowed to die in prison (mainly the former, totalling about 285), from 1555 to 1558.
However, Mary's executions began earlier than that. Mary came to the throne at the head of a rebellion against her cousin Jane Grey, the "nine days' queen", in 1553. Almost immediately afterward, she had Jane's father-in-law, the Duke of Northumberland, executed as the ringleader of the usurpation.
Mary's entry into London showed how popular she was in comparison to her cousin, and how eager England's Catholics were to see her bring back the old religion: she was quite clearly victorious and secure on her new throne. She could afford to be lenient, and she generally was, allowing Jane, Jane's husband, and his brothers to live on in imprisonment in the Tower of London without actually ordering their executions. However, after her impending marriage to Felipe of Spain was announced, a revolt known as Wyatt's Rebellion arose against her - partly nationalist (to the extent that we can use that word about the sixteenth century) and partly religious, an uprising of Protestants who feared the marriage as heralding a kind of Catholic and Spanish invasion, and it was a real threat to Mary's life and crown. While the leaders and ninety participants in Wyatt's Rebellion were put to death, she granted pardons to 600 captured militants in a show of queenly clemency that her supporters praised. It was only in its wake that she finally condemned Jane and her husband to death, as her councillors had been urging for some time to protect her from further rebellions that wanted a Protestant ruler.
Mary's persecution of Protestants specifically for their Protestantism didn't begin until more than a year into her reign. In a letter to Cardinal Pole in December 1554, she described her plan for going forward.
Touching punishment of heretics, we thinketh it ought to be done without rashness, not leaving in the meanwhile to do justice to such as by learning would seem to deceive the simple. And the rest to be so used that the people might well perceive them not to be condemned without just oration, whereby they shall both understand the truth and beware to do the like. And especially in London, I would wish none to be burnt without some of the Council's presence and - both there and everywhere - good sermons at the same.
This is certainly more extreme than anyone today would think appropriate for religious differences. However, it's also far from the stereotype of Mary as a zealot who came to the throne determined to cleanse England with a purifying flame. She was determined to repress Protestantism, but the religious demographics of the country were not such that it was a solidly Anglican population living under the oppression of a tyrant; in fact, rather than a purge of "Anglicans", many of those executed were radicals of various kinds who were also offensive to Foxe and other proper Protestants. Apart from the initial, high-profile burnings, they were also in large part local affairs conducted by local authorities in response to local concerns. Much like persecutions for witchcraft, accusations of heresy were lobbed at neighbors as part of ongoing disputes.
As noted above with regard to Wyatt's Rebellion, religion and politics were highly intertwined at this time. To be of a religion differing from that of the state was frequently to doubt the legitimacy of the state; in this case, Protestants considered the marriage of Katherine of Aragon and Henry VIII to be invalid (since the pope didn't have the authority, in their eyes, to approve the consanguineous union) and therefore Mary a usurper who killed the true queen, Jane, and was displacing the next appropriate heir, Elizabeth. Mary had faced the prospect of possible execution for religious belief herself in 1536, for her unwillingness to agree with her father that she was illegitimate, and in Wyatt's Rebellion she was at times extremely close to the fighting. Exiled English Protestants abroad even called for her death. The repression of Protestants was therefore as much about protecting Mary's position as it was about forcing people to come back into line with their religious beliefs.
The other Tudor monarchs were also not known for restraint in dealing with threats to their throne. Henry VII came to the throne by fighting a war in which Richard III was killed, and would later face a number of small rebellions: the Stafford-Lovell Rebellion in 1486, which was small and resulted in the execution of Sir Humphrey Stafford; the pretender Lambert Simnel in 1487, whose loss at the Battle of Stoke resulted in the deaths (in battle) of Francis Lovell and John de la Pole (a descendant of Edward IV); the pretender Perkin Warbeck in 1495-97, which resulted in the executions of Warbeck and Edward Plantagenet in 1499. (And those are just the deaths of leaders - I am not certain how many below them were executed after battles.) Henry VIII dealt with the last potential Yorkist heirs, executing Edmund de la Pole (John's brother) in 1513, Henry Courtenay and Henry Pole in 1538, and Margaret Pole in 1541.
Things got bloodier once the Reformation was underway. 1536 saw the Lincolnshire Rising and Pilgrimage of Grace, Catholic rebellions in the north of England that gathered tens of thousands of people who objected to Henry VIII's behavior; the Rising's leaders were executed, and while the Pilgrimage was too big to stop, when it was followed by/morphed into Bigod's Rebellion in the following year, at least 144 people were executed, more if one includes people related to the Lincolnshire Rising who were caught up at that time. A small plot that coalesced around resentment at the punishments for these risings resulted in about fifteen executions. Under Edward VI, the southwest would erupt with rebellions over a combination of religious, political, and economic causes, with massive casualties; Buckinghamshire and Oxfordshire also rose up and were suppressed, with executions of ringleaders. Even Elizabeth would face the Northern Rebellion, a relatively bloodless attempt to install Mary Stuart on the English throne - and despite the lack of body count, the queen ordered 700 of the rebels executed (though the number actually killed is not clear).
So the burnings that occurred in Mary's reign should be seen as part of a continuum of state-enacted violence to protect or ensure the legitimacy of the ruling monarch. (The Tudor period, and really 1400-1600, was just a terrible time to be in England.) She was not uniquely bloodthirsty, although the fact that these individuals were killed by burning does stand alone as a particularly horrible and overtly religious method of execution. The Tudors were very unstable on their thrones, and continually faced threats to their rule that they needed to oppose with weapons of war.
A huge part of the representation of Mary as this vicious tyrant hated by an oppressed Protestant populace comes from Foxe, and from the traditional Protestant historiography. "History is written by the victors" is not actually a natural law, but in some cases it does hold true - and the fact that Protestantism is treated as inherently more enlightened and a step on the road of progress in English history is one example. The truth is rather more nuanced and Mary actually came to the throne with a great deal of popular support as the True Queen who was returning the religion of the people to the land. Many appreciated her religious processions and ceremonies and the improved commercial relations between England and Spanish territories after her marriage, and were elated when she first appeared to be pregnant and when English and Spanish forces beat the French. Her supporters portrayed her as a just ruler and even her critics tended to portray her as someone led astray by false counsel. At the time, the burnings were not necessarily seen as something that she was doing (and even now there is scholarly debate over whether she was the primary mover behind the official policy or one or more of her councillors) and did not characterize the period until the seventeenth century.
Some sources for further reading:
Sarah Duncan, Mary I: Gender, Power, and Ceremony in the Reign of England's First Queen (2012)
Anthony Fletcher and Diarmaid McCulloch, Tudor Rebellions (2008)
Linda Porter, The First Queen of England: the Myth of "Bloody Mary" (2008)
Alexander Sampson, Mary and Philip: The Marriage of Tudor England and Habsburg Spain (2020)