He has to share everything. Nothing in his life is his. The only good thing in his life is probably Bug.
He's getting upset because he has to share something of his (horses) like he has to share the rest of his life. While sharing is a good thing to do, this boy has had nothing to call his own so I can understand his posessiveness.
I would sit down with a glass of Kool-aid (presuming he doesn't like coffee here) and talk about Bug with him. Tell him he's doing a good job with him even though you don't think he is. He's feeling threatened that you might take the only good thing in his life away from him. Thank him for riding him for you while you were away. Tell him how much Bug likes him and that you've noticed.
Even if none of this is true, say it. He needs to feel secure and he needs to feel like you aren't the enemy.
After you soften him up a bit, talk about how you would like to share Bug equally so he gets ride time and so you do. Tell him you don't want him to feel left out, but you don't want to feel left out either so maybe set up a day by day schedule as to who rides him (you get Monday, he gets Tuesday, you get Wednesday and so on) or set up an hour schedule for each day (he gets the morning, you get the afternoon or vice versa).
This is an under privileged kid you're dealing with. He needs to understand that you don't want to take Bug away from him. You'd just like to enjoy some time with Bug too.
And those who were seen dancing were thought to be insane by those who could not hear the music