the woman who donated him does not want him back and does not care what happens to him (her words).
Based on this alone, I think there was a reason why this horse was donated. People are shady and often try to dump their problem horses on others.
Ten minutes into the ride he was doing all the "normal" things (whinnying back home and to any other horses we passed, stopping occasionally but easy to start back up, gently trying to turn around, etc.). We stop because my husband had to tighten his cinch a little and I figured I might as well check mine too, which definitely needed some tightening but it was still a comfortable fit. I go to get back on and before my butt hits the saddle he immediately turned to go back home so I try to gain my balance and correct like I did several times and suddenly he goes straight into the air and bronc bucks. Needless to say bronc riding is not a career path for me. He bucks all the way back home and I send my husband on his horse to make sure that he makes it back since he had only been here a week and I walk/run back.
Now back at the house, I lunge him for 15-20 minutes until he joins up multiple times easily. No bucks or anything the entire time he was lunging and again he is very responsive to my body language. He isn't whinnying anymore to the other horses and he seems to be back to the horse that he was when I rode in the arena the first time. So I go to get back on and again before my butt hits the saddle he is spinning and up in the air and I am back on the ground. I repeat the lunge and remount one more time, this time with my husband holding him, and same results (i.e. insanity). At this point I decided I was lucky bruises were all I was walking away with so a bruised pride was going to have to be the final blow. I ended by doing ground work with him, which again he was an angel for.
Maybe he's cold backed and needs some "time" after you tightened the saddle on the trail.
Maybe when you got back into the arena, he knew he got you off the first time and so he did it again.
-My first thought was saddle fit because it happened after I tightened the girth. I checked his back after the incident and no sore spots anywhere, not even minor ones, but to be safe the next time, if i get the chance, I will use a different saddle.
-He just had a veterinary check when she bought him and he is "healthy as a horse"
-He could be barn or buddy sour
While I agree these are things to be mindful of to make sure the horse is comfortable, I also believe these are NOT excuses for the horse and he should still NOT be exhibiting this behavior.
What exactly did the vet check, actually check? If it was just a quick check of vitals and not an actual lameness exam, you could start with a lameness exam and see if anything shows up. Checking for lameness when you have a known problem like this, I think, lets you know if there are any pain issues that need to be addressed before working on it as a behavioral issue.
If he passes the lameness side of things, if you feel like you can "stick" his bucks, then try again, keep his nose turned to you as you get on (maybe have a helper) and be ready for him to take off. Once you get some control over him, then work his @$$ off. I absolutely do NOT tolerate bucking, especially bad bucking like this, and I am not afraid to show to the horse that I am displeased with them and they made a very, very poor choice.