Transitioning to the Big Bathtub

It's fine to bathe your baby in the kitchen sink or the baby bathtub until she's simply too big to fit. By then she should be able to sit up on her own and you can start using the big bathtub. It's a good idea to get some non-slip mats to put down the floor of the tub so your baby stays put without slipping. Also, don't fill the tub too high with water; keep it to the level of her belly or so.
It's also a good idea to get some floaty toys to keep the baby entertained while in the tub. You may also want to get a kneepad for yourself so it's more comfortable as you kneel over the tub.
And of course as you well know, never, ever leave your baby unattended in the tub or near any water.