What is the longest amount of time you can keep your BP out of it's enclosure?
Depends on what the snake is used to and what it seems to be ok with. As you get to know your snake you may pick up on their body language and be able to "read" when they are stressed.
I handle my BP regularly for a hour or two at a time. She seems to have no problem going over 3 hours when she wants but I can usually tell when she wants to go back in her cage because she'll actually just sliver over to her cage on her own. Or she'll try to sliver away from me. But if she's just sitting on my lap or chest not trying to go anywhere I don't see the need to disturb her after a specific amount of time to put her back in her cage.
Obviously if she's hissing at you or trying to get away or curling up into a ball or trying to strike she's not happy about something.
My big rescue ball python Fluffy is my "ambassador snake"
he's content sitting around my neck or on a chair for hours.. 4 -5 and then some. Once I put him on my neck.. he's fine in the car.. getting out to go to the Redbox at McDonalds.. and I take Fluffy to a bar/grill a few doors down from where I work often when it's warmer (there's an outside deck where my friends and coworkers sit).
Snakes to me are like nailpolish..there are just SO many beautiful ones I have to have!
The main thing to think about is that they are a cold blooded creature so they need something to say warm. If they are against your skin they could stay out for a pretty long time. Just don't let them roam around your house, get cold, slither in dust and hair, etc. I can't say what the longest amount of time they could stay out and stay healthy, but if you keep them warm enough I would say they should be fine as long as you want to babysit them.