Totally agree with Duffman on the biting issue but this didn't seem to be a bite or attack.
Shouldn't be a problem rehoming him as it wasn't an aggressive action. Anyone who knows collies knows this behaviour, and would be happy to take him.
This was a herding nip. I'm sure he warned her, and warned her again (head and ears down, tail up, dancing side to side and barking). But due to her ignorance of dogs she continued to advance (or maybe even run which is the worst thing to do) which elevates the dog to the next level, sneek behind and then a nip. This is the herding instinct. This is not an attack. He didn't want to fook her up, just get her moving out of his garden. Which in fairness he did.
If he is not neutered get it done ASAP.
This often helps reduce the territorial side in them and also a lot of other undesirable behaviours.
Also argee with Duffman in that the dog should not be roaming around the gate. In the photo you have an electric fence collar on him? Does the boundary allow him to access the gate? Seems to be partly your fault and partly her fault due to a slight lack of knowledge of the breed.
Not really the dogs fault as Duffman has also siad.
Have a look at this link which explains the nipping much better than I can. A lot of good stuff on Border Collies here
http://www.bcrescue.org/nipping.html
Again, really hope it works out for you and your pooch