I haven't taken the jeep to the mechanic yet about the spring but I have experimented successfully with another solution. :idea: This solution came from Bounty Hunter.
It's common, my YJ does it when you have too much foot on the pedal. Back your foot off the gas pedal to where you're just using your toes to operate the accelerator. You will no longer have the weight of your foot on the pedal and it won't bounce over the rough stuff.
I have moved my foot down on the gas pedal so I can see the top half of the pedal (I can see the top of my shoe when I look/glance down) and the problem goes away! The shifting is smoother and there is no bucking over bumps. :D
My son was also having problems driving the jeep, so I told him to lower his foot on the gas pedal and his problems went away too. :D It is a little weird driving with just your toe on the pedal but I'm getting used to it.
I think I'll still see what the mechanic has in mind so I can have a little more freedom in where I put my foot.