I probably shouldn't be posting since I haven't got a Tamagotchi Music Star and they haven't come out in my area yet and I'm just judging from what I've heard. Apparently you only raise one character at a time on a Music Star as opposed to the v5's "raise three to five characters." So I'm presuming that since you're not raising a whole Tamagotchi family you don't have to raise their bonding. Another thing I've heard is that you have to raise your Tamagotchi's tone, rhythm and originality. I'm guessing this is kinda like skill points on the v4.
Don't take my word for everything I've said because it may not be true.