I never ever for even a second left them alone. Yes that means hugging a naked dripping toddler soaking my nice shirt while I ran down the hall to get a fresh towel.
These are the 4 steps I did when moving my daughter to the tub at 8 months
(1) i bought a bath mat similar to this
http://www.amazon.com/Extra-Long-Vinyl-Bath-Mat/dp/B001I7PY1E/ref=sr_1_1?ie=UTF8&qid=1349495828&sr=8-1&keywords=bathmat
(2) I kept the water level not higher than the top of your foot
(3) I sat on the edge of the tub with both feet inside. that way, in case my little one stood up or fell, my legs can become an extra support.
(4) lots of toys/plastic books to keep her busy so she doesn't stand up
http://www.amazon.com/Sesame-Street-Bubble-Featuring-Monster/dp/B003TT3B9G/ref=sr_1_1?s=baby-products&ie=UTF8&qid=1349496123&sr=1-1&keywords=bath+books
I fill the tub up a bit, keep the faucet running, and then pop him in with me (I don't actually bathe with him -- I remain standing wearing a t-shirt and shorts). He can still splash around and have fun, and I can get him clean pretty quickly. Sometimes I get pretty wet, other times not at all....
Hope this helps.
We used a bath chair inside of the big tub starting at about 6 months, when the babies were old enough to sit and have head control. By 12 months or so, they were too mobile for that so just washed them in the big tub. The main thing is to stay close, don't leave for any reason for any amount of time until a little older. When my eldest was almost 3 yrs olds and we had her baby brother, I would make her sing to me if I had to go out of eye sight for any reason. I would never be out of hearing range and only left for quick needed exits.
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Hi -- For what it's worth, we never used a baby tub -- always gave the baby a bath in the regular tub. At the beginning I'd get in with him, until he was able to sit up well on his own. Lots of cool toys are key to keep them engaged and not wanting to stand up or scooch around. There is a Yookidoo spout that is a little $$ but an awesomely entertaining bath toy -- you can find on amazon.
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UPDATE:
BIG thanks to all of you who took the time to reply to my post asking for advice on moving our son into the big tub for bathing. We did our first bath in the big tub tonight and it was a huge success -- E. absolutely loved it and behaved brilliantly. He was ready! Again, thank you!
H.