There is no way I could've done it in a normal bath either.. Firstly, we don't have one! Secondly, I guess the only way you'd be under the water is if you were on your back, and there was no way I could've birth on my back. If you have a bigger bath, like spa sized or a corner bath you could probably do it.
The birth pool I used was a blow up one... Um.. LaBassine or something? Deep enough so that I was squatting and my tummy was completely underwater. It wasn't that big really, but deep. The area we had it set up in was about 3m sq and there was plenty of room. I know the wooden ones are much bigger. I loved the blow up one as the edges were like a pillow to lean on.