Speaking as a shifter, a deep bow like that woman just used implies a trust that the other beast is not going to aim for your neck at the moment you become vulnerable and look away from them.
At least, that's what our instincts tell us. Never breaking away too far from some of our primal thoughts, despite our higher thinking capabilities.
Pure humans in my kingdom had a different way of displaying respect. Looking down, but not away, while holding their palms over their core.
I can only say that something about both sides' methods strikes me as more respectful than… showing your belly. Wolves treat a position as submission that a feline regularly proves the determined can fight from?
More claws to dig into flesh. So silly.
Though maybe that is just the royal in me avoiding the idea of any unnecessary submission.
"Well, let's dig in, shall we?"
Or just the fox mentality I was born with, that likes to make others work for it. The chase, the tricks, the lures.