How about providing her with a general idea on where, what and
when?
Where - so she know what to wear..
What - so she knows what to expect/do from this outing..
When - so she can plan her time..
Ask her in a casual way.. as you are asking your friends..
Leave the response to her, if the activity interests her, she
will go.. even as a normal friend..
All great things start small :)