how long can i expect tile paint to last on a bath and vanity
The longevity of any paint job depends on so many factors; it is my opinion is that this question is too broad (see the How To Ask page for details).

That being said, you will get the longest life if you:


properly prepare the surfaces to be painted; that means thoroughly sanding all surfaces and perhaps acid-etching the "bath" (if by the term "bath" you mean a porcelain coated bathing tub) if recommended by the coating manufacturer. Note- this is the most important consideration, hence is listed first
apply the paint exactly as directed
use the best quality applicators
use the highest quality paint product


The conditions the coating will be subjected to will also determine longevity, such as moisture, light, cleaning methods, human contact, etc.