I'm posting this as question even though I have a valid workaround, mainly to help other people who might come up against the same issue. However, if anyone knows how to fix it correctly, feel free to reply!

I had a strange problem starting up BASS: on startup it would immediately minimise to desktop, but sound would still be audible. It would allow me to maximise it for a moment, after which it went back to the desktop. After a few tries I noticed my media player (MediaMonkey v4.0.6) behaving oddly during the attempt, so I closed it. Apparently that fixed it: I can start and play BASS normally now - I just have to remember to close MM every time I start it up, which is a bit obnoxious but not showstopping. Anyone have an idea what is really going on here?

Have you tried reinstalling BASS?
Also I would suggest just keeping MediaMonkey closed if that's the problem or maybe try a different media player, if you don't feel like closing down MediaMoneky each time you want to play BASS.