anyone who has experience or thoughts about this.
Experience - not with pole beans in pots but I did bush beans. I push it when growing things and, if you stay on the watering, 3 or 4 bush beans in a 12" pot can work.
Thoughts - Pole beans in a 12" pot won't work. Pole beans get big and the 12" pot won't have the root zone you need. It will be stunted and the production will be limited. If you were in the ground I would say 2 plants in a 12" circle is leaving a bunch of room as I plant 2 or 3 beans per string and space the strings every 6 inches.
Can you simply knock out the bottom of the pot and place it on the ground letting the roots grow into the ground?
I think 12" pots for anything other than things as house plants (or hydroponics) are too small to bother with. The exception to this is if you cut the bottom out and let it be open to the ground to create a tiny raised bed. I cut out the bottoms of 8" pots and put them on the lawn for growing tomatoes when I was a renter.