When my daughter outgrew her infant bathtub we just moved her into the big bath. We bought one of those no skid mats for the floor and put it down. Even before that I usually just got in the tub with her to give her a bath because the little plastic tub was such a pain in the butt to deal with and clunky to store so I just ended up getting rid of it. Just a no-skid suction mat and my two arms.
This is the exact mat I have: http://tinyurl.com/2bb685
I liked the foamy texture rather than those other bubble plastic mats that looked like they'd leave dents in a little tush.
Just like with a little bathtub, make sure you never turn your eyes for a second because a second is all it takes. Only fill the tub up a few inches.
Now that she's 16 months she likes more water in the tub to splash around in and practices putting her face in it (and not sucking it up her nose).