>So would you assume at this point that she’s most likely gone over, so we’ve missed it? It doesn’t seem too likely to me that she will become interested in him again and he, her.
Not necessarily - because the other explanation is you were trying too early, and the stud dog was trying his luck to see if she would let him. Now he knows he won't be allowed to mate early, he may be biding his time. It is often the case that the dogs can be completely disinterested until the bitch is fertile and then they are suddenly raring to go. And indeed, some successful matings happen as late as day 28 even. (I think someone on the forum here had one then.)
But I'd also agree that giving you the stud dog to manage all this is very weird. When you pay a stud fee, you're paying for the service as much as anything - that's not just the semen(!) but the management of the mating and the dogs. Giving you the stud seems very irresponsible and careless for him as well - studs can be injured during mating if not managed and they can't assume that all bitch owners are going to know how to manage things.
Furthermore, studs usually feel more confident on their own territory and they also come to associate a particular routine with a girl coming to visit. Ie - getting put in the utility room whilst the girl has a look round, coming out and smelling her pee in the garden, then being introduced to her... it all works as psychological foreplay and communicates to him what's expected so that when he meets her, it can be a bit like a bull in a china shop and that tends to overcome any telling off a bitch might try to do - he is so uber-confident by then.
In a different environment, that whole routine isn't going to be possible and he won't feel as confident away from his familiar home. Especially if he is timid anyway, as you say.
So it's very unusual all round for the stud owner to do this... It would be better for them to board your bitch rather than the other way round.
For now, keep trying them together on a daily basis but only for 20mins or so and then separate until the next day - till she goes out of heat. Just in case you were early... OR - as suejaw suggests, go to your vet and get a progesterone run now so you can see where she is in terms of ovulation.