Although that '79 Cadillac is after GM downsized their full-size cars in '77, it's still a 4300lb car. You might have it secured to the tow dolly, but it can still be "interesting". IF you can find a universal bumper-mount hitch, remember too that the energy absorbers on the bumper mounts (between the bumper and the frame) will probably compress and release some as you slow down or stop. That "stroking" of the absorbers will allow the bumper to move too, which can affect the integrity of the bumper fillers (which are flexible) as they're now about 40 years old and probably still in pristine condition.
The other thing is that bumpers are considered to be very stout. After all, they are "bumpers". But they can still flex and bend! Which can compromise the durability of the chrome plating! There's a reason that bumper-mount temporary hitches went the way of the rented overhead roof-mount cargo bin! U-Haul didn't like paying to fix customers' vehicles from the damage those things generally caused to them.
For towing anything heavier than a red wagon, the Class III receiver hitch (usually welded, sometimes bolted-on) is the best way to do things -- period. The old Class I bolt-on hitches were rated at 1000lbs tow weight.
End result, you could end up doing some expensive damage to your car in that 20 mile distance. Damage that would cost much more to fix than the cost of a roll-back wrecker! Plus, it'll usually decrease your anxiety level, too.
Call a AAA-service tow truck and pay the price. It'll probably be more reasonable than you might suspect, by observation. It'll be done quicker and easier.
CBODY67