depends on what the activity is. personally i love Rock climbing.
It's perfect! if she agrees, great! if not, works out for me as well since partnering up there is real easy. you can meet alot of cool people there.
Typical Interaction
"Hey, i was actually going to rock climbing place on thursday, i get the feeling you'd like it."
She replies something like
"Rock climbing? I've never been."
blah blah blah
"Sure! sounds like fun, what do i need?"
Or
"Oh i wanna go but i work/school/abduct cows from a farm that day"
"That's fine, i go often and you can partner up right there, give me your schedule and if any dates line up soon, we'll go."
If she declines.
"Nah that's ok, i work/hold seances/do my hair that night and besides i'm not sure it's right for me."
"To each his own, i'll just partner up with one of the athletic young women who work/go there." <---- something along these lines to know i'm not going to be there on my own. whehter it's a friend or whatever.
Depending on what is it your going to, this can or cannot work. I mean, going to a movie or an amusement park isn't a good choice for this style.