"I don't know how many times I've heard "bottoming out" used since hitting Blighty's palsied
shores. Whatever happened to "getting to the bottom of"?"

Dear CK: To me "bottoming out" means to be approaching a low level, as when stock market values rate of decline becomes small, and an upturn seems likely.

"Getting to the bottom of" to me means accumulating enough evidence to give an answer to a problem.