No matter what commercial product I've tried, the bathroom sink would get clogged. I'd clear out the trap but the clogging was further down. A snake only made a small hole.
My cheap remedy:
Pour half a cup of baking soda, then half a cup of vinegar into the drain. Quickly close the drain so the fizz would stay in the pipes. One hour later pour a kettle of boiling water down the drain.
This cleared up the pipes instantly and I have had no problems since.
Maybe for the tub, double the doses.