Boldcomic, it depends who we are riding with. If I have friends who want to stay in rooms at Ruby's inn, We stay in the horse motel at Rubys' in. They have a nice facility for the horses, lots of room for the trailers. And we can eat their buffet meals instead of cooking. Those wanting some ammenities get a room at the Inn , others may pay to park their trailers in the camp ground where they can hook up.
But more often than not, I prefer to camp out in the trees someplace away from the crowds. There is a nice Forest Service equestrian camp at the end of the Coyote Hollow road. Just before the Upper trail head for the Thunder Mountain trail. It has 5-6 spots and hitchen rails to tie the horses at while you camp.
I've also just pulled off the road into the trees near the entrance to Losee Canyon. Just put up a highline for the horses. It's primative camping and nobody charges any fees. Losee creek usually has water running in the spring for the horses to drink.
Most folks ride/hike the Peak-a-boo trail in Bryce Canyon itself or the Thunder Mountain trail in Red Canyon. Both are great trails and someplace that you should see at least once. But there is so much country around Bryce and most folks just don't have any idea. By riding some of the out of the way trails, I get away from all the tourist.
The rides up Losee, Casto canyons and Butch Cassidy draw are just as spectacular as the trails in the park.
I also like to camp up Corral Hollow. There are lots of stock pond for the horses to drink out of. And most of the riding is thru Ponderosa forest. You loose a lot of the red sandstone, But it is still a great place to explore