Don't know if things have changed that much but when I was a reservist on active duty, one of my buddies went from reserve to USN in a couple of weeks. We were at sea and they sent of a msg to CINCLANTFLT and he was given the oath in a week or two. I suppose that it depends on how bad they want you.
Have you done your 368 Request to go Active and the Request Chit to your CO?
Make sure that you have an UNDER-MANNED rating on the Active side if you want to go over. I would say the latest Creo would tell you, but there doesn't seem to be one since last Sept. nearly a whole year ago.