All of my children, as babies, fell asleep as some point or another in their bouncers.

I do not think it does them any harm at all.

I didn't use a bassinette at all: we opted for a hammock. It may be, that if if Madeline likes the motion of a bouncer, that she may sleep beautifully in a hammock?

Worth a look anyway:

BellyBelly Product Review - Baby Hammock