Except in some very particular situations (maybe you're looking for investors in your coffee roastery tech startup), getting coffee is a means to an end, the "end" being the same thing as the "ask" that DelaneyM is referring to.
"Hi $name, interested in grabbing coffee?" buries the "ask" until during the coffee chat.
It can be tough to do, but I think a lot of very busy people would actually appreciate you just coming out and asking for what you want, even in the first sentence.
"Hi $name, interested in grabbing coffee? Bla bla bla I met you bla bla, bla bla talk about bla bla."