No, I'm afraid BSPlayer doesn't. It uses "external" text-based subtitles.
So to BSPlayer there is no added value whatsover to have (static!!) subtitles "burned" into a movie. However if you feel you need to change an avi-file so that it has fixed subtitles (so that they will also show on other (less flexible) players): the method I describe in
this post works fine for me.
(VirtualDub for avi-movies and VirtualDubMod or VirtualDubMpeg for mpeg) (adicoto's method probably works fine as well, but I've personally never used it)