Medievalist, that is the problem with one word posts.
For the record, I would usually write master's degree (or degrees). My point is that someone who writes masters is not making a mistake, although some people might regard it as erroneous. You can write whatever you want and it would not bother me since, with or without the apostrophe, it would be correct in my book.
The MLA style guide is one of many. It is predominantly humanities based, which is fine - but don't assume it is better (or worse) than any others. I would point out two things, however. Firstly, I have never come across qualifications being listed in a bibliography (despite the multitude of formats adopted by the various journals). I think the MLA style guide will specifically recommend against those. Secondly, the punctuation is usually omitted after the qualifications nowadays (I think this is probably a recent thing).