Easy and quick answer for you is to google bambinipronto. That is the supplier of gro bags here.

I don't have a gro bag for Abbey, just couldn't afford one. I do however have a Snug Time bag for her, which is the same principle as the gro bag. Abbey wears an all in one suit and singlet under hers and yes, I still use some covers on her.

That said, alot of other ppl don't like to use the covers. So I guess it's up to you and your bub.