How to get rid of shaking and bouncing while driving? Permanent solutions?

Being that you just purchased the truck, it could be possible that what you're experiencing is not abnormal for this vehicle. What was your previous vehicle? This is a truck with a truck suspension, made to sustain loads and abnormal road surfaces. Sure, you can replace shock absorbers -- at 11 years old, it's time anyway and may help a bit. You may also want to have your tires checked for age and wear -- are they possibly causing some of the vibration? Perhaps they need balanced? Also, it's a good idea to have your wheel alignment checked -- even angles that may not be adjustable should be measured to see if components have been bent and can cause ride concerns. Use this link to find some shops near you that can help with your concern: www.repairpal.com/repair-shops