If you're bowel incontinent and have pooped in your adult diaper in public then you just go into the restroom when one is available and change the poopy adult diaper like you would at home.
Just be sure to throw the poopy diaper in the trash and don't leave it in the toilet stall.
If you don't have a clean diaper with you then you'll need to wait to change the adult diaper when you get back to your vehicle or wherever you put the diapers.
It's best to keep some clean adult diapers in your car or other vehicle so that you never forget to bring a new diaper.
When my kids were in diapers I would keep a few diapers in the glove box and some diapers in the trunk of the car so that I never went without diapers.
For a kid I would change their diapers sometimes in the back seat of the car or in the trunk of the car.
If you have to and can fit you can change your adult diaper or someone's adult diaper in the backseat of a car but cover the windows so nobody can see.
With a kid you don't have to cover the windows unless you want too.
Just put a changing mat or towel down on the seat and then lay down and change the poopy diaper.
You might have a hard time sometimes getting all the adult poop off you and if so just get the most of the poop off you as you can and then put a new diaper on.
Then go home when possible and change the diaper and shower.