Regarding just the phone call to discuss the trip: I don't think you're "obligated" to initiate the first phone call for any reason, but since she says she's lost your number and has directly asked you to call, I think it would be a little odd if you emailed back and said, "Here's my number again. YOU call ME." If she says she doesn't have your number and wants YOU to call HER, I don't see what good it would do to "wait for her phone call"--why would she call when she's expecting a call from YOU?
I get the feeling you are a little wary and uncomfortable with her as yet, which is completely reasonable given that you've only met recently and don't know each other well. Personally I would not want to put myself in someone's house for three days in a distant place, totally dependent on them, at this stage of the game. Just because you think she's generally a decent person, doesn't mean you'll be compatible with her personality/lifestyle.
I would thank her for her generous offer, but say that you would rather get to know her better first through other methods, and ask her what the best method for that is--Facebook, email, phone, etc.. Make sure you're not the one always initiating contact, the electrons go both ways. Then maybe someday when you feel more comfortable with her you guys can seriously discuss an in-person visit.