
Usual practice is for the bitch to travel to the dog, ideally on the day she's ready, which can be the 10th day, but can vary tremendously. My bitch wasn't ready to mate till the 18th day for her last litter! Personally I'd also be very unhappy about leaving my bitch with a stranger.
If I were you I'd work out which of the three dogs was most suited for my bitch in regards matching bloodlines, take her to the vet for premate tests to determine the date of ovulation, and take her to the stud within a couple of days of ovulation. If she still wasn't standing, I'd bring her home and try again a day or two later.