If the library is reliable, you can assume it works. From the look of it though I wouldn't expect it to be very reliable so having a few tests to check that you get the expected results would be good.
It will also help you understand clearly what output you can expect from the lib - for example are the dates plain strings, are they date objects? Are the numbers actual numbers, or strings, etc. Know your data basically, because it's central to your plugin. Also later when you invariably hit some edge cases, you can add more tests specifically for these.
As for your questions, I'd just test one bibtex file, as long as it's representative enough, and that's it. It doesn't even have to be a file, you can add the bibtex data as a template string into the test, and that way you don't need logic to load a file.