It can take up to 10 days for the member to get the confirmation letter from MS, although it usually comes sooner. (Sometimes, it takes even longer. I think the member just doesn't want to make promises he/she isn't 100% sure can be honored.
Why not ask him/her to fax (or email if he/she has a scanner) the confirmation to you when it arrives? That would at least save the mailing time between you and him/her.
Otherwise, unless your trip is very soon, ask if you can wait to send money until after you get the paper confirmation.
If your trip starts 9/15, it is entirely reasonable for the member to ask you to pay upfront before even making the ressie. Reservations made within 30 days of arrival are more risky for the member than those with a longer lead time.
Best wishes -