A hyper horse might also be an unfocused horse, and based on that little information tidbit, i'd recommend the following:
Before you pull him out to ride, go out into the arena and scatter cones, jumping standards, bending poles, and random ground poles all over the place. Then as you get into the arena on his back work bending him around and over these obstacles. Have a good mix of upright obstacles (jump standards, cones, speed event bending poles) and ground objects (poles) and constantly keep him interested and in tune to you by twisting, turning, and going over the objects. Not only will this help him focus, but you will also have a more supple horse because of all the bending and steering.. this is how we taught Skippy to neck rein.. the arena was full of jumps and jump standards, so we just turned and circled all around them and within a week we had a supple well bent neck reining 4 year old! =)
Also, the obstacles -might- help keep him from bolting, since there will be no clean "path" to run in without hitting an object. Of course, not all horses think when they bolt.. so thats why i made sure to put emphasis on the "might help" :p
When he speeds up with trotting keep bumping him back lightly with the bit. If you ride with spurs or a crop i would definately recommend not doing so for this particular horse at this point in time. Make sure -you- are the one in control and -you- are the one setting the pace. He just needs to listen and respond =)
And as for the two step aspect of the bolting, my best recommendation is to ignore it. Don't rake his face, stop him, or punish him. Almost pretend like it didn't happen and keep pushing him through and maintain the nice working trot.
And the fact that he is more spooky with you in the saddle shows me that he is insecure of being alone on the ground. Our horses tend to get a "security blanket" feel for us, and when we arent next to them when we are teaching them something new, they don't like it because they feel if something bad happens they will have to react themselves since we wont be right next to them to help... if that makes sense.
Im sure i forgot something... but thats the gist of my advice i can give ya on what I know of the situation. Ah, the fun of riding a 4 year old!! =) I hope this helps ya!