Is there an adapter that allows you to hitch a trailer to your vehicle without a permanent vehicle mount?

Other answer:

I remember years ago that U-haul provided them with trailers so you could tow their trailer with your Oldsmobile. They attached with chains tightened around the bumper. As others say, back when bumpers were non-crumple metal. Our 1970's Olds was designed so that the jack actually fitted under the bumper to lift the car, which as I had just arrived from the UK I found totally weird (along with the foot-activated handbrake and the gas filler pipe hidden under the rear numberplate).

Some pickup trucks still have strong bumpers, and you can get a towball that bolts right on to the step in the middle. Canada (at least) requires that there also be somewhere to attach safety chains.

Back in the day when cars had real steel bumpers, there were, but now that bumpers are plastic, not a chance. They have to go up under the back end to find something structural to hold on to.
Dimo J:
All commercial trailer hitches are bolted on, hence can be removed.
Yes, but not safely. When bumpers were actually metal you could get one that bolted on, but they tended to loosen up on you. Today with plastic ones…well…
A thought shared.
Only if you have the adaptor permanently fitted to your car.