The first time I tried riding him in the roundpen he did great. Then then next day I tried the arena. He bucked and bolted. I took him out again the next day, when a couple other riders were out, and he did even worse. So I tried lunging him in all four corners of the arena, no one else was out. He did a little better, still bucked a few times but every time he did I would make him trot even longer and faster. He seemed to understand that behaving badly ended up in more work for him. And after a few days of this he did not buck once and seemed more comfortable. So I tried riding him again in the arena (just walking) and he did the same, bucking and bolting.
I went back to the roundpen and he did great.
This is my first horse and im running out of ideas of how to help him. Any advice or help would be really helpful.