The dog is the one doing the work, and he needs to be confident. Generally, breeders want the bitch to come to them so that their dog is on his own ground.
In reality though, if you have an experienced stud dog, he can manage the dog in your back yard, in his house, behind the barn in the fair grounds, at the hotel close to wherever the show is that people are entered. And to hear some of the old time breeders talk, their dogs have done it in all of those places and many more.
As for doing this thing naturally, I hope that you are not set on that. These dogs are not going to live together for the rest of their lives. Some bitches will bite the dog when he starts doing what he does to make this happen. You might THINK your bitch won't, but there is no way for you to KNOW that unless you have already bred her. Getting bitten by a hard to breed bitch can be bad for the dog. You really don't want that to happen.
Also, the dog and bitch will tie, and at that point it is USUALLY safe to remove the muzzle. But you cannot just let them trapse around the back yard. An old time breeder friend told me of a story she knew about, where the bitch came in heat in the middle of the winter, so the people stayed inside while the dogs were tied in the back yard. There was a stone wall in the back yard and the bitch jumped it and did a lot of damage to the male.
What actually happens, is the dog owner and the bitch owner hold the leads while the dogs are tied, and wait patiently until everything comes out ok. Sometimes getting to the tie point is interesting. The stud owner sometimes has to position the bitch and then help the dog get where he needs to be.
For some reason rangy, mangy border collie mixes can leap tall fences in a single bound, open kennel gates, get through garage doors, can soundlessly manage to accomplish the deed without getting bitten, or otherwise injured. And every time he calls, he manages to father a healthy litter of 12-14 pups that all survive, all while eating a crappy diet of Old Roy.
Jenna, RN CGC & Babs, CD RA CGC HIC
Heidi, RA CGC
SG3 Odessa, SchH1, Kkl1, AD
Ninja, RN CGC & Milla, RN CGC
Joy, Star Puppy, RN CGC
Dolly CGC & Bear CGC