When Chloe was really small, I used to just take a bath with her. I would put a hand towel on my legs and lay her on that, and I didn't have to worry about slippery baby syndrome. The bigger she got, the more difficult this became and eventually I had to come up with a new plan. Once she was able to sit up on her own, I discovered something that really works for me! I use a dish pan. I still do it in the bath tub, so splashing and just general bathing doesn't create a big soggy mess. I have found this to be really fast and easy for multiple reasons.
1. It's fast because I don't have to fill an entire bathtub.
2. It's easier to get it the right temperature. If it's too cold, I empty some water and add more warm water. Too hot? Empty some and add cool water.
3. She can't go anywhere, and there's really not even room for her to fall over.
A couple other things I find helpful...
I put her towel on the bouncy seat in the bathroom. When she's done in the bath, I just take her out, set her on the towel in the seat, then wrap her up and go. It's so much easier than trying to juggle her and the towel. I don't have to worry about dropping her, (man wet babies are slippery!) and I don't have to worry about her getting cold while I'm juggling.
I wash her with my hands and I use a normal full size wash cloth to wet and rinse her. It works especially well on her hair. She doesn't have much hair yet, so this could be why it works well. She happily puts her head back when asked to, I put one hand under her chin and help her tip her head back and with the other hand I dip the wash cloth in the water and then ring it out in such a way that the water goes down the back of her head and not in her face. Since it's less water than if I used a cup, if any does go in her face, it's not much and she doesn't seem to mind.
This system has really worked for me! For more great tips, visit Works for Me Wednesday at Rocks in My Dryer.