Ford F250 4x4 vibrates when it hit's a bump and then doesn't quit until you come to a stop or hit another bump

Check the front end for looseness. Especially the tie rod ends and cortrol arm bushings. Also check for any play in the hub bearings.

check you springs you may have a broken spring also jack the wheel up one at a time and check the bearing hands 9 and 3 pull side to side and then up and down at 12 to 6 any excessive movement and the bearing needs changing. do this to both wheels. also check the anti roll bar rubbers all 4 of them check for splits or wear this can also make a clunking sound on bumps of any size. failing all these you may need to have your disc's checked as they may have become warped can happen if you use them alot ie hills, sudden stopping

try a simple fix of putting injector cleaner in the tank to clean the injectors
check for any loose body screws and panels

I had this happen in my old dodge stratus. My trick to remove cd's was when you stopped or parked the car turn vehicle off and hit the eject button and it will usually eject the disc. remove all discs and then install them again when car is parked and not moving as vibration and bumps while driving can sometimes miss align the disc in the player. Sometimes when the stereo didn't work at all I disconnected the battery and it would reset and work. If this doesn't work it may be broken. Good Luck.

Vibration from about 40-60 mph is usually attributed to wheel balancing, but the onset when you hit a bump seems to indicate play in the steering linkages (tie rods etc) or suspension members and stabiliser bar rubbers but you had that all checked out, that brings us back to the wheel balancing.

Check all motor and trans mounts

Check drive axles for play and wear

could be a bad brake caliper, try riding brake and hit a bump did it quit? loose exhaust system, boken strut or shock, broken sway bar stabilizer bolts

cehck tie rod ends on steering. Or loose suspension part.

i would be checking the lower ball joints if they arent replaced soon they will come undone at the worst time and you will then need a tow truck or flat bed

The heat shields that are positioned between the exhaust pipe and floorboard or between the exhaust pipe and sensitive electrical components are made of very cheap, thin, tin-like metal. When they rust on one side, one of the tabs comes loose and the whole shield will vibrate especially when accelerating. Since you are getting the noise when you hit a bump, you might check the area where you stow the spare tire (loose tools may be vibrating against the metal). Also the plastic protective pieces behind front bumper sometimes tear and will "flap' against the car and sound like a metallic vibration when you hit a bump especially if you were stuck in snow recently. Look for loose plastic pieces.