Agree that if you're trying to arrange something exclusively (at least at first) through AW, it's best to commence correspondence several days in advance, because you can't always count on a response in time to set up a same-day. As also mentioned, it seems proper etiquette to email first, suggesting the type of booking you're looking for, duration and so on, and giving a preferred time for the appointment.
I've noticed that it will often help, if you're able, to 'offer' several alternative days/times in the initial email. I've had messages read, but ignored, if the WG is already booked up - bit rude, imo, to not even bother to say, "Sorry luv, not available!" - but I'll usually get a positive reply, leading to a booking, if I can suggest more than one possible slot.
All depends on the girl, but I've been using a combination of calls/texts and AW to make bookings lately. If she wants phone contact first, fine, I'll do it that way, but I'll also send a parallel email and eventual booking request once the meet is agreed. I'm still interested in gaining (positive!) AW feedback, to show that I'm legit and not about wasting her time, so I'm happy to deal with the inevitable delays when emailing.