Giley,
I know you said that you have already potted on your beans, but for the future, the magnificent thing about peat pots is that you din't have to remove the plant from the pot. Just pot into a larger pot or the ground intact. Give a good soaking and the pot will gradually break down and become a built in fertiliser. The roots will just carry on growing through the pot until the pot gives up - no root disturbance!!
Many grapes here are very anti peat pots (they come from an unsustainable source - but so does petrol, gas and most of the UK's electricity!!!!!) I think they are great though..
Good luck with the runners.
Tx