Short answer:
Yes.
Discussion:
first we have to get the dates straight. The "middle ages" is a name we give a period, sometimes it's useful, very generally it's from the fall of Rome to the fall of Constantinople; that's the thousand years from 476 CE to 1453 CE; other people may prefer different dates, but that's the ballpark.
The "Bubonic Plague" you're likely thinking of, often referred to as the "Black Death" to distinguish it from other plague events, occurs in the mid 14th century. So it essentially occurs at the very end of the period we call "the middle ages", and as such can't "influence" the art that came before it. There _were_ plagues earlier in the period, including the celebrated "Justinianic plague" (541-42 CE, affected the Byzantine empire), but they did not have as dramatic a demographic or social impact. The "dead people lying in the street" ugly plague that you're likely thinking of is the "Black Death".
This plague is then followed by subsequent outbreaks of plague in Europe, into the 18th century; but by that point we're well out of what anyone defines as "the middle ages".
So, bearing in mind that the event you're asking about occurs very near the end of the middle ages, did it have an influence on the artwork of this time?
Yes. We can see it in artwork -- the danse macabre / dance of death / memento mori. Starting in the 1420s we've got paintings -- many of the earliest now unfortunately lost-- devoted to the idea of the impermanence of life and the possibility that death looms everywhere. This subject proves very durable, inspiring artists from Durer to the present to paint "Death and the Maiden" for example; we've got five centuries of artists painting this subject, and we've even got music inspired by that painting (Schubert most notably).
We see it in literature -- Chaucer in The Pardoner's Tale, Boccaccio in the Decameron. And of course Petrarch (Francesco Petrarca):
In 1348, when Petrarch was forty-four, the plague suddenly removed several of his best friends, his chief patron, and his beloved Laura. In 136I, when it recurred, he lost his son and his closest friend. It is fair to say that the plague was an outer circumstance that made special demands on Petrarch's consciousness. Nino Sapegno sketches the role of Black Death in Petrarch's life: '. . . from the terror and sadness of those days, [he derived] a sense of weary self abandonment in God, and even more, a need to meditate on his past life from above and to judge it severely in its vanity'. Of the sonnets concerned with Laura's death, he says, '. . . there appears again that insistent examination of conscience, that concern with meditation and reflection which is the most profound source of poetry in the earlier part of the Canzoniere as well; and now it appears . . . with a more desolate and weary kind of harmony. The sense of death pervades these confessional passages and colors them with a languid sadness, lifts them finally to a supreme longing for peace.
As Petrarch is one of the key figures in the emergence of the "humanistic" sensibility -- as well as the modern Italian language-- the events which shaped his experience of existence, communicated through his writing, become an important part of the literary developments that collectively we call Renaissance humanism. Parenthetically its Petrarch who popularizes the term "Dark Ages" for the centuries prior to his life . . . but he did not think of himself as living in them; he might well argue that "the middle ages" ended in the 13th century, eg before the arrival of the plague.
We see it in music: there's advice from physicians that music may keep the plague at bay.
We see it in ecstatic public performances, like flagellants beating themselves in the streets, and various plays based on the danse macabre.
The topic is huge and depending on just where and when you're interested in, much more can be said, but your TLDR is "Yes", and these themes stay with us into the modern era, indeed into the present, even if the connection to the plague is sometimes lost.
So we have medieval instantiations, like Edgar Allen Poe's The Masque of the Red Death - although Poe doesn't say so explicitly, his details all suggest the plague which Petrarch lived through. And we have vaguer references, like photographer Robert Maplethorpe's celebrated self portrait with a cane carved into a skull. Some of these subsequent references are rooted in the plagues of the 14th century, but some are based on later plagues -- in Maplethorpe's case, he's appropriating old symbols for a modern plague, AIDS. Similarly, Daniel Defoe's celebrated Journal of a Plague Year, written in 1722 is _not_ about the medieval plague, but rather about an outbreak that occurred in London in 1665-- this was "bubonic plague", but presumably not the bubonic plague you were referring to in your question.
Sources:
Bús, Éva. “‘Death's Echo’ and ‘Danse Macabre’: Auden and the Medieval Tradition of Death Lyrics.” Hungarian Journal of English and American Studies (HJEAS), vol. 14, no. 1, 2008, pp. 83–93.
Gertsman, Elina "The Dance of Death in the Middle Ages: Image, Text, Performance" (Brepols:2010) [unfortunately out of print and very hard to find, ruinously expensive in the used book market).
Gertsman, Elina. “THE BERLIN ‘DANCE OF DEATH’ AS THE ‘LAST JUDGMENT.’” Source: Notes in the History of Art, vol. 24, no. 3, 2005, pp. 10–20.
GIRARD, RENE. “The Plague in Literature and Myth.” Texas Studies in Literature and Language, vol. 15, no. 5, 1974, pp. 833–850.
Usher, Jonathan. “Boccaccio's ‘Ars Moriendi’ in the Decameron.” The Modern Language Review, vol. 81, no. 3, 1986, pp. 621–632.
Gilman, Ernest B. “THE SUBJECT OF THE PLAGUE.” Journal for Early Modern Cultural Studies, vol. 10, no. 2, 2010, pp. 23–44.
Chiu, Remi. “MUSIC, PESTILENCE AND TWO SETTINGS OF O BEATE SEBASTIANE.” Early Music History, vol. 31, 2012, pp. 153–188.
Watkins, Renee Neu. “Petrarch and the Black Death: From Fear to Monuments.” Studies in the Renaissance, vol. 19, 1972, pp. 196–223.