Well my advice before asking them out at a specific time would be to ask, "Do you want to do something sometime?" Its a nice broad question. If she says sure, then ask for a specific time.

Its seems to me that shes being sincere when she talks about this all-girl slumber party, so my advice would be to just let her do that, then ask her again some other time, but don't say something like, "what are you doing on saturday?" its harder to interpret if shes really busy or just blowing you off. Say something like, "You wanna do something this weekend?"