Ok, so maybe the thing about horses who appear to have a protective "bubble" around them isn't that they have a bubble but that they lack a bubble.
Here's my thinking:
Once, when I had an episode of depression, I was prescribed an anti-depressant. As I began to feel better, I noticed (which I hadn't cottoned onto while depressed) that my sense of self had shrunk internally to the point where "I" did not quite extend to the outer edge of my epidermis. As the medicine took effect, I found that I began to "fill" my own body until "I" coincided with the physical space I filled. But it didn't stop there - that sense of life (as opposed to the cold world "out there") continued expanding until I was coated with a protective bubble wrap. I called it my "magic bubble." And it kept growing, until I began to feel that it had spread to cover the whole world, with me at the center.
One of my daughters has a strong dislike of having her personal space invaded. She becomes depressed easily. She dislikes dogs - probably because they are much more headlong in their approach to a person. She likes cats and horses. She dislikes having her space invaded not because she has a bubble, but because she has no bubble to protect her. An unwelcome touch from the outside brings the cold, hard world directly up against her being.
Yesterday, hanging out with Gus and Skipper, I found that Skipper projected a welcoming warmth. Perhaps that is his bubble. He's happy to have you come into it, because it protects him as well as the person entering. Gus, perhaps, has no such magic bubble and so likes to meet you head on. Perhaps his assertiveness is the closest thing he has to armor.
Our George also dislikes having his personal space invaded. Like Gus, he does not care to be scratched or groomed. Again like Gus, he prefers to interact using his head and face and mouth.
Perhaps instead of asking the horse for permission to enter their bubble, we could try suggesting to the horse the possibility of developing a bubble ..... ?