I know the bubonic plague is thought to be originally from somewhere in asia, carried by the trade and travel the Mongol empires set up. This means, presumably, it affected China, which was a society with extensive writings and contact with the Mongols. Do we have contemporary accounts of plague around the time of the black death in Europe, if not, why?
The question of where bubonic plague originated is a live one, historiographically speaking, and it's by no means clear that the earliest outbreaks we know of – the Plague of Justinian in the sixth century and the Black Death in the 14th – did in fact begin in east Asia.
The problem was covered in several earlier posts – led by /u/y_sengaku, this thread offers a good guide to this discussion and while you are waiting for fresh responses to your query, that's where I'd suggest starting.
I'm not a historian, but I've done a fair amount of work on this history of infectious diseases. In short, yes, there was writing, but the preserved written records are not particularly helpful, not just in china, but generally, since people didn't practice medicine in a way that allows doctors now to identify the disease, and even if they did, those details weren't usually reported.
For China in particular, a recent paper by Timothy Brook, a historian at UBC, discusses this. In the response, quoted in part below, Brook's paper explains why the extensive writings that existed in China aren't helpful for answering the question, and why historians think it came from China. (Spoiler: they have genetic evidence.)
After discussing lists of plagues compiled based on administrative data, the paper says: "Whether any of these disease entities is Yersinia pestis [i.e. Bubonic Plague] is impossible to determine from the documentary evidence alone. They could be plague, but they could be the diseases we know as cholera, measles, dysentery, or smallpox, although smallpox was separately designated in traditional Chinese medical terminology as dou. Historians are cautious about retrospective diagnosis, lest this approach predetermine what we are trying to determine (6, 7). However, recent advances in bioarchaeology now make it possible to identify relationships between aDNA and the disease entities we know today (8). Particularly persuasive for this historian is the recent research reconstructing a genealogy for strains of Y. pestis based on core genome analysis (9). That research has identified a polytomy or “big bang” in the branching of genomic mutation and dated it to 1268, with a 95% confidence interval between 1142 and 1339 [see Green (10) for discussion]. The dating is striking, as it just predates the eruption of the Black Death in Europe in 1346. The findings also strongly indicate that the original plague reservoir was in the Kokonor region along the northeastern edge of the Tibetan massif, which places the disease adjacent to transport routes along the Silk Road." (Amusingly to me, at least, Brook notes that he's a historian, responding to epidemiologists, while I'm more of an epidemiologist responding to a question posted to historians. )
(Side note: I looked for data on this to inform a paper I wrote on estimating risk of natural pandemics - https://www.liebertpub.com/doi/pdf/10.1089/hs.2018.0039 (pdf warning.) It turns out there is frustratingly little good data on the topic in general, and the records we have are likely to be incomplete anyways. But those are issues I discussed in more depth in my paper.)