Our dog bit me last year. He bit me on the lip so badly I needed eight stitches under general anaesthetic. It was partly my fault in that I put my face near to him when he was sleepy, he was spooked and simply snapped without warning.
We couldn't keep him, although it wasn't really his fault, it could have been one of our children next time, or one of their friends, and there would have been a next time. He had bitten my husband before, but he was still a pup then and we thought we could handle it.
We were lucky to find a couple with a small-holding and no children and he went to live with them. Last we heard he was happy. He was really the loveliest dog.
We told the people he went to everything. They saw my face. They were experienced dog owners and were confident they could give him a happy home.
We spoke to the Dogs Trust, they would not take him because he had bitten. I fear this means that many owners are dishonest about their reasons for rehoming and the rehoming centres are being filled with biters and aggressive dogs.
OP, it's a horrible decision to have to make, you have my sympathies.