No number, no booking or meet.
In my view exchanging numbers is essential - what if either of you need to cancel or contact at short notice or just inform the other party you are running a few minutes late?
If she refuses to share a number or talk prior to the actual meet, I would move on and find an SP that is more willing to share contact details.
Another thing to consider... what if she arrives with a couple of blokes, they rob you and leave? You will not have her contact number or address in order to pass on to the police, and she can easily delete her AW profile.
Not saying that would happen, but maybe something to consider given she seems very reluctant to provide any details about herself outside of an online profile, which by the way already seems suspect if she states she is happy to speak on the phone, but then refuses to do that or share a contact number.
A lot of WGs and SPs like to get a 'sense' of a client by speaking to them prior to a meet as a part of their screening process, and not just rely on AW message exchange. She seems to not be bothered by this which strikes me as a little bit odd/unorthodox, especially for an outcall.
Do you have her AW link? Maybe some other clues there that more seasoned members may pick up on?