Original pre-'98 F-series bed bolts are carriage-type, with long square or oval bosses under the heads. Even if they don't spin during removal, they often break due to rust. New replacements are not available (as of the upload date), but newer-style bolts CAN be made to fit with almost no modification.
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This bolt spun, so I welded a temporary grip to the head. After removal, I removed the grip, and welded splines under the head so it couldn't spin again. But it's a lot of work, and requires even more damage to the bed, so it's not a good solution.
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Don't forget to remove any OTHER bolts holding the bed down, before attempting to lift it off. But to make this swap, the bed barely needs to be lifted - just one side at a time, and just a half inch is enough.

These aftermarket bolt kits are affordable, and good enough, with 8mm Allen (hex recess) heads. At least 2 short and at least 2 long bolts of at least 6 bolts total are required; the other 2 can be either length. But some short bolts are not threaded as far up, so look for those with a noticeably shorter unthreaded shank. Genuine Ford bolts are much more expensive (new, but common & nearly free in JYs), but higher quality with T50 heads. Genuine nuts are 1-piece, and threaded properly.
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Aftermarket long bolt dimensions in mm.
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Aftermarket nuts included with bed bolts are crimped too much. If they're simply installed, they'll spin in their U-clips. To prevent that, chase each one with a lubricated bolt (anti-seize is what I use) before installation. Note that the vise is gripping the socket which holds the NUT - not the U-clip.
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I sometimes use this portable gantry (made from scrap metal: a 5" Aluminum I-beam, some 1.5" straight square tubes, and some 2" square tube T's, with common 5/8" hitch pins to adjust the height) with a 12V ATV winch for outdoor lifting. It could have even been powered by the truck's own battery, but I wanted to be able to set the bed down and drive the truck without it. To lift pickup beds, I use a common 2x4 cut slightly longer than the width of the bed under the lip (so it can't spin in the bed) with a heavy screw eye in the center. A few test-lifts to find the balance point take less than a minute before it can be lifted high.
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Lifting the bed this high is NOT necessary simply to swap bolts. But this truck was getting a lot of other work done.

After thoroughly washing the frame (and whatever repairs prompted removing the bed are completed & checked), install the later-style U-nuts (chased with anti-seize) on the frame so the bed is easier to remove next time.
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The hole over the axle needs to be enlarged just this much for the later bolts to fit.
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Lifting the bed is easier than it sounds - it doesn't weigh much, and an empty one can be lifted by 2 strong adults. But a 12V ATV winch on a portable gantry is very convenient & relatively cheap, which is what the top left pic shows. A 110VAC winch costs about the same.
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If the bed is tilted as in the lower right pic, don't let it slide off the frame, or pry against the bumper. I chained the bed to the frame before tilting so it couldn't slide or shift. But to ONLY change the bolts, it doesn't need to be lifted as high as shown - that truck needed fuel tank work.

But it doesn't need to be lifted this high or tilted this much JUST to swap to the later-style bed bolts & U-nuts. These trucks were all getting MUCH more work done.

Undercoating the exposed threads will protect them from rust, without interfering with removal.
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The front Left bolt is hardest to see because of the front tank (if equipped).