Back in the saddle - advice?

Unfortunately that tends to be the way, unless you are an accomplished competitive rider or trainer, you'll get the dregs of the barrel as far as horses available to ride. It's always the owners that can't ride the horse themselves, but don't want to sell, that will offer them up for people to come and ride!!

Attitude, bad riding, and hind end lameness and/or back soreness can all be reasons for a horse to not want to work properly on the bit, engage the hindquarters, collect,etc.

As said above, there can be many reasons for a horse to throw a rider, and it might not have been soley due to being asked to come into the bit. And , at that time there could have been other health issues. Who knows.

I would ride the horse several times and feel him out. Watch him move and see if you can detect any lameness/soreness issues that would have been the reason for his bucking. ASk regarding his dental care. Look at the bit used.
YOu ride and move him little by little into some connectedness to the bit. No horse likes or can do it overnight, especially one who has been ridden strung out for years, so do it compassionately and feel for his mental reaction to this change.

If you can lunge or round pen him you can get a feel for how he deals with pressure.

I would be inclined to investigate a bit further and give it a go.

I went out to ride him today, and he was off. His owner decided to pull his shoes yesterday, as he had thrown one and she thought he'd be sound barefoot.