How large a tub are we talking about? Are we talking about the standard contractor's narrow tub found in 90% of homes or are we talking about one of these large sunken tubs that you can swim around in?
Perhaps we're all thinking of the contractor's narrow tub while you're thinking of the olympic pool sized tub.
If the pool sized tub, I can easily see why you'd want to be displacing a lot of water and there are probably some ready solutions for that if it isn't confined to the size of a standard narrow tub.
Basically, is your tub the size of the one with the couple in the tub full of rose petals or is it the size of the tub where the man is providing his own bubbles?