In online cooperative, the game does not in fact cycle when clients kill a boss, so I'm unsure how to reproduce this issue. Also it's not the case that Bubba and Bilsy use the boss2.j2b: any boss may use it, depending on how the Activate Boss events in the level are configured. Bilsy does not appear in any official SP levels, so I don't know what level you're testing this in. I did try, as a client, defeating Bubba in hell.j2l a couple times, and Xmas Bilsy in xmas3.j2l, with music turned on, but didn't experience any crashing, even when the server manually cycled by typing /r or /c.
Are you running any mutators that may have caused the crash?
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