I have not heard of a boy asking parents first if he could date the girl.. I think he is first trying to make sure she even likes him.. In our family, we always invited the young man over for a meal and an evening of board games..
This allows everyone to get to know him. And for him to know how much we love and respect our daughter. Then if we felt he was a nice young man, we were fine with daughter dating the young man.. Most of the times now days, kids today go out in groups.. Lots of kids meeting up for a movie, the carnival, school events..
Just keep open communication. Make up rules about week day and weekend curfews.. About driving, about calling with updates and change of plans. Make sure they are enforced. Let her know you trust her to be a good girl and to stay safe.
As long as you all speak openly and respectfully, this is good opportunity for you all to stay informed on what your daughter is up to and who she is friends with.
One hint, We were a group of parents that watched out for each others children.. We made agreements that if our children were to embarrassed or could not get a hold of us for some reason, we had "Safe Parents" they could contact, that would pick them up from whatever place no matter the situation with no questions. They would bring the child home. This happened to only one child. She had been at a party that started to get out of hand and she went outside and called a mom (not her own) and asked that she take her home.. She just wanted to talk it out with the other mom, so she would not upset her own mom.. It ended up the girl had attended the party and some kids started drinking. It frightened this girl. She just wanted to be able to cry without her mother seeing how scared she had been.