You are going to be *very* unpopular. No professional pilot likes their livelyhood being cheapened by what you propose. Most FBO's already have instructors that have arrangements to use their aicraft.
And, no, insurance won't come with the aircraft rental. Especially not professional indemnity insurance or equivalent. Do you not understand the purpose of the FBO's insurance? It's to protect the *FBO* from renters! Not you.