In your example I merely see one rider who knows the horse better than the other. That doesn't really constitute a bond in my mind, just that you happen to have more experience with a horse than your friend does. And vice versa, she has more experience riding her horse than you do.
*shrug* While I believe that yes, a horse with a bond to a specific rider will do exceptionally well, I wouldn't consider that horse to be as well trained as one that can go brilliantly with any well-versed and well-schooled rider after a handful of rides by said different rider. All horses have their quirks, it's more the fact that someone who has been riding a horse for longer will know those quirks and the horse will know that they know those quirks. My horse is a good example of that. He's a fabulous jumper, but he's lazy and he's clever. Any time someone new gets on to jump him he will try to refuse or run out. Hell, he even does it to me if he hasn't been jumped in a long time. However if the rider makes sure he gets over the jump that first or second time he won't do it again. After that he's a dream for whoever happens to be on him. I wouldn't consider any person who he does refuse for to have less of a bond with him, and just because I can see it coming a few strides away doesn't show that I have more of a bond with him, it just shows that I know him better than the person riding, which will happen whenever someone whose been riding a horse for 5 years watches someone else riding the same horse for the first time.
Don't get me wrong, I like to have a bond with the horses I ride, but I'm not going to say that the reason I didn't get as good of results as say the owner or former rider in a show is because I didn't have a bond with the horse. It's because I wasn't riding my best that day and it's my fault for not being more on point.