Aaron..depends on air flow, temperature and humidity.Anywhere from 3 or 4 hours to a couple of days. You can tell when they are dry by feel (they'll feel like crackly paper) and they will have shrunk and probably ripped off some of your tacks.Once dry remove from boards and cut offf the belly scales. Roll up and put in a plastic bag (like a sandwich bag) if you are going to store them for awhile before using.
What kind of bow? Wood or glass backed?
I like to put my skins on before I put a finish on the bow.
Tite Bond 3 will work just fine for gluing them on for a wood bow, not sure about glass backed bows, but I imagine it would be alright for one of those too.