Briefly, you want to present yourself to hospitals as an agency, just like any other agency. You can ask them what bill rate to use as a starting point, you may actually be pleasantly surprised. I know I have been! Before you talk to HR about contracts and so on, you will want to do it from a position of strength, meaning the manager already wants you. Either you have worked there before and they like you (best), or you have wangled a mini-interview with the unit manager and the upshot is that she wants you. Now you can negotiate and get around the first thing they will say, "We are not taking on any more vendors". That is the most difficult thing about doing direct contracts, but there are a dozen agencies or more at every hospital that get through this obstacle.
There is an FAQ you should read before coming back here and asking questions. Search Google for "NedRN Independent Nurses". I just did this and the third link is the one you want to read (you will have to navigate to the beginning).