Can I use bentonite as a lining for a normal swimming pool?
Bentonite clay at the bottom of a pond does not form a hard surface that could be walked on. The clay layer will be a goo which is virtually impenetrable  to water, but absolutely unsuitable for walking on. If you were going to do this, I think you would have to have a layer of sand or gravel on top of the bentonite layer.

How common is a "natural" swimming pool where you are? Have you researched how to prevent the growth of the amoeba Naegleria fowleri? https://www.mayoclinic.org/diseases-conditions/naegleria-infection/symptoms-causes/syc-20375470