Those mats are a great idea. Only one piece of advice--take the mat with you as you look at tubs & make sure it will stay stuck to the bottom of the tub (especially if the tub has a non-skid bottom). We tried the mat in our last house and it wouldn't stay stuck to the tub bottom--sometimes it would seem stuck, but then once you added water it came unstuck.

I have to say I bought one of those air mats a few years ago, I think it was a Conair, and took advantage of the store's return policy after using it once. Noisy and not very effective; same problem with large bubbles I've described elsewhere, wasn't relaxing at all. I've seen microbubble generators that look like hand shower heads, except that it's an air hose connected to the pump which sits on the floor outside the tub, and the bubbles spread out from the nozzle which you dip under the water and aim anywhere; think that approach may work better. Can't find who sells them, they work like the one in the Youtube link below except that one looks like it's for a commercial tank of some sort rather than a bathtub, but same idea.

Here is a link that might be useful: air bubbles