I first thought that "bubble" bath meant some air bubbled through the
water from below, as it is done in so called "jacuzzis" (right?)
In this case, the bubbles would carry away a lot of heat, because
the air has to be saturated with water vapour.
Now, Petes and Jons answers
deal about some more or less stable foam layer on top
of the water. In this case, the evaporation of water at the surface is
blocked, the heat loss from evaporation (main loss in a bath tub!)
does not occur.
Plastic or steel or cast iron tub is secondary, when the tub is
"built in". But maybe that is something specific for Germany?
For a free standing tub, on the outside the heat transfer is
ruled by air speed, the tub material is not so important in most cases.
Georg