My Shetland Pony, Bluegrass, Nearly Always Refuses Jumps When I Am Riding Without A Saddle. Why?

This may be because you are not as stable in your position as you would be in a saddle, therefore you'd be losing contact and impulsion.  Try to sit exactly as you would if you did have a saddle.  

Also sometimes it's easy to bounce your hands around while bareback, so you may be jarring him in the mouth.  

Remember that when you approach a jump you must hold him/her inbetween your hand an legs to help him get his stride right and lessen the chances of him/her running out.