Every dog is different so I can't say whether a month is an average amount of time.

I can say, that I see the "run away and don't come back until I'm ready" thing A LOT in dogs that are never allowed to run free. It's like, they are finally free, they don't want to go back to the restrained feeling again until they have had their fill. Regular runs until he is ready to come back will help with this.

Let him run in a fenced area until he is good and done. You can just walk the perimeter until he decides to come to you. When he does feed him. Once he has gotten more energy out and is just basically following you but still sniffing around, you can start backing away and showing him the food you have. AS SOON as he starts towards you say "Yes", when he gets to you BIG party down reward, then let him go again. He will get better and better and soon he will realize that just because you are calling him in does not mean you are going to put him on the leash, but that he will be rewarded and allowed to go out again. This is also a perfect time to work on some off leash commands, like sit and down, then reward and let him go again. When you are done, and he is tired, call him in, give him a command to let him know that you are done like "enough" or "we're done", then leash him up and head home.

Thanks for the advice, Niomi!

My dogs dragged 20, 30, 50 ft long lines around for quite a while, even when first on e-collars out on the fields, just to be sure. This way they were able to be free but I still had an element of control if I needed. I would get the dog used to a drag line at home before going out & about with it. My pups start on them from the very begining, so it is something they grow up with. But any dog can get used to dragging a line.

I would not let a dog that doesn't already have a pretty good recal loose on a line out where they can take off. I would definatly work in a fenced area for a while. JMO Empty tennis courts, paddle courts etc in the evening might be a thought if you are looking for a place that is fenced but a reasonable size to start off in.

I will also say that a month with a new dog is not IMO sufficient time to really bond with a dog. It usually takes a number on months for that to truly happen. It would be sooner with a very young pup & later, in most cases, with an older dog. But I am sure that there are a few exceptions to this.