Ive got one of these Jess.
Bath seat
Its great as it supports them well if they cant sit up totally on their own and it also swivels all the way round, so you can just twizzel them round if you need to to wash them n stuff. I got mine for a tenner if asda baby event. It says not to fill the bath over about 4 inches, but ive always filled it up to the normal height which is prettyfull. The seat has suction cups on the bottom so its not going to float off or anything. x