He'd never kick at her, and she isn't afraid to be close to him... good tip... when I was alone and she would drag I kept letting the line slip until I was at the end of it.
If she starts to drag, turn - into her so she has to turn maybe. Don't go in a straight line all the time, that will also slow Bay's walk down just a bit. And please be careful - she sounds like she'll be okay but we've had horses, generally the babies try to rear up or bite since their head is right at your knee.