How do you get crowded bean plants out of pots?

You could try dunking the pot contents into a bucket of water and gently washing the roots apart.

I'm no expect but I would plant them in clumps. Rather than risk damaging them I would leave them as they are.

But they need to be separated as they will be growing up a wigwam bamboo structure. One to a cane.

Is that right?

Yes. That's what I've been doing today and it's easier than it looks!

Years back I got some from Wyevale that came like yours and planted then in clumps rather than separate them out and they came out fine, although they were dwarf beans rather than climbers.

Have you already separated them?

I usually plant mine in clumps and they seem to grow fine but then I use netting.
Why dont you put some netting around your wigwam or use garden twine tie it at the top of the wigwam and spiral round till you reach the bottom and tie it off that way there is more support fro the beans to ramble across.

A few years back I planted some peas(my first ever batch of peas).When they all came up they were more then "slightly" overcrowded.Because they were in a seed tray,I just cut the contents into rows of peas.
You don't have to have 1 plant per cane,there can be some more(without going mad).Give them some additional support(netting or some cotton string tangled on the canes will be fine),you'll have a very "bushy" bean spot but they'll be fine

Could you plant the clump in the middle of the canes, or to one side, and then train each bean vine to its own cane as they grow? (i.e. gently pull it over towards the cane and perhaps tie it loosely till it gets the idea and starts going up)

Not that long! I sowed some climbers last week and they are already 3" high. They get away really quickly in this warm weather.

It is possible, I have done it on a number of occasions, but it is a fiddly job.
Make sure the pot's contents are moist (not soaking wet).
Have newspaper or sheet or something to work on, and work at waist height. (I've just done a pot for my niece and stupidly crouched to do it
- killed my back!)
Don't attempt to pull the beans from the pot. You need ALL of the contents, not just the stalks.
Squeeze the pot from the outside to loosen it. Put as much of your hand round the top as you can without squashing the plants, and tap the bottom.
Hopefully, the contents should slide out. If not repeat. If they still don't come out them put some thin like a plant label down the side and run it round.
Tip the pot gently onto your sheet. There will be a solid mass of roots.
Now the tricky bit. Using a plant label (or pencil) TEASE the roots apart, making sure that each plant has its original bean. You are unlikely to have much compost around each bean so support the root/bean and gently lay it flat on your newspaper while you check it.
Get them planted as soon as possibly since they will dry out quickly without the rootball.
Firm them into the ground VERY GENTLY as they will not have the support of the root ball and if you press down too hard you actually break the seed bean away from the roots.
Depending how tall they are, you may also have to worry about unwinding them from each other before you start.
I grew far too many this year and ended up with around 30 plants that I had to dispose of. Some of them were around 18" tall but sturdy.
I live in Essex and my niece lives in Surrey. Last Thursday I carted a load of them on three trains, and a bus journey to her house. All in individual cardboard tubes that I had made the day before.
OH was horror struck when he realised what size we would be transporting.
Got them there in one piece though and my sister was a bit miffed that they were stronger, taller and healthier than her GC ones.
My daughter took the rest which pleased me as I really didn't want to put them on the compost heap.
You can do it if you have patience. Hope that helps.

Thanks for that help, guys and gals.

I haven't got them out yet- I will do tomorrow.

They are around 12" tall, and pretty sturdy, but are in need of support.

The seeds that I have sown have shot up almost overnight- they are now around 2" tall already. I only put them in last Monday. I'm going to leave them out in direct sun throughout the week, and probably plant them the 2nd week of June.

Will update you tomorrow.

I wouldn't faff about - I'd chuck 3 canes around it and plant it as is.