I should add that if you can find an NSF for Bubble Bobble (and I'm sure there must be one out there somewhere), then that should contain the exact same code used in the ROM – just re-arranged. If you can figure out how to make changes to the NSF, then you can make corresponding changes to the complete ROM. But that will make it only marginally less of a pain in the neck.
While some programs like Famitracker can make NSF files, you can't use those in an arbitrary ROM without replacing the sound engine, as previously noted.