I'm running a 5e campaign with a group of three PCs. One PC rides a Griffon and I typically struggle to effectively run combat when she is in the air and the other PCs are on the ground. She spent several quests working toward this goal and it's actually lead to some very fun role-playing. I'm just trying to make combat less clunky.

Here are my specific questions:

1. How long would it take for a flying creature to make a pass at an enemy? (either diving for a melee strike or shooting with a bow from the flying mount)
2. What counter-strike abilities would the person on the ground have? Must the bide initiative and take a swing as the person is diving?
3. What modifiers would be appropriate in this case?

My thinking is a person on a flying mount should have a substantial advantage vs. those on the ground. However, I think that the ground enemy should have some recourse if attacked by someone on a flying mount.