yes, indeed there are supports for a bathtub. you need to research this because it is very important for the stability and the "fall" of the tup for drainage.
There is a 2x4 that rims the entire enclosure that the tup rests on its three sides. This is installed at the level of the tub and is applied with a level or accuracy. The tub will have a lip on the three sides for this 2x4 to rest on. Then the tup has shims or wood buildups that the tup sits on.
most tubs come with a built in "fall" or angle to cause water to drain properly from the tub to the drain hole. Check into this.
Please research this procedure carefully prior to reinstallation of your tub.