What are the customs decal and eAPIS requirements for flying to the Bahamas?
AOPA has a useful guide to flying to/in the Caribbean, including the Bahamas. To answer your specific questions:


You do need a customs decal if your aircraft is considered private by the CBP, regardless of whether you own it or rent it (I've seen them myself on several aircraft that I've rented)
eAPIS is a system for reporting who is on board an aircraft every time it crosses the US border, it has nothing to do with the decal