Getting rid of fleas for good?

Hey all! Some tenants just moved out of an apartment my partner's parents own and we were looking at moving in. They had a cat. The place is FULL of fleas. When we walked in to clean, they started crawling up our legs. We flea bombed it last night (hot shot brand, just whatever they had at Lowe's), and when we get back this morning we're gonna throw out anything fabric or upholstered and flea bomb it again. We're tossing the old mattress, box spring, couches, curtains, etc. We also don't have any pets. Can we do anything else to kill them faster so we can move in sooner?