We had a problem a while back when a relative's cat came in daily for a few weeks and had fleas. I think we got somebody out to spray the main areas and it solved the problem. Might be worth trying the bug bombs first since it it sounds like they will do the same thing.

For the bites, we have a product called "Anthisan" in the UK, it's an excellent antihistamine that works very quickly on any sort of bite or sting, we are never without a tube. (active ingredients: mepyramine maleate and benzocaine)