Hi Vaasu, I don't think it's possible with the “tune” music in Bitsy, but I played a game with music added with the “bitsymuse hack by Sean S. Leblanc” and music does not stop during dialogs. I never tried any hack, but hope that can help you!
Viewing post in Music gets interrupted dialogue
Hi, so I modified the html file for the game a little bit to add the music from external audio files. It's not a super clean way to do this, but it works if you're just doing something small like I was. Essentially, I checked the room transitions and if the player was going into a specific room, I would change the music.
First at the bottom of the game's html file, I added this code so there's audio element with an id that I could call.