can anyone tell me when is the right time to move and re-position my bay trees

Couple of questions first - is that growing in the ground and how long has it been in situ? If its more than 3 years, and certainly if more than 5, you're taking a big risk trying to move it - you would need to keep a massive rootball and even then you'd break some roots. If you were going to attempt it, though, winter, when its dormant, would be best - but by the thickness of that trunk, it looks like its been there a while...

Sorry - didn't read your question properly, I'm tired, not concentrating - you say they've been in 5 years - I wouldn't risk moving them, personally.

I agree with Bamboo, you'd be taking a big risk if you moved.

I beg to differ people. . .
The whole point in moving anything is so often because a plant is unhappy or the gardener (for whatever reason) wants to move the plant.

Your pictured plant looks happy and healthy and looks like its getting the nourishment it needs.

However, if you still wish to remove it - you can - only wait until November if you insist. Do try to move as much root ball as possible. Consider the root ball is a mirror-image of the clipped foliage area - so your ball should just about fill a builders' wheelbarrow.
Don't water-it-in wherevever you put it. It should be pouring everywhere by then. . .

Disagree strongly with your advice to not water when newly moved, Muddywellies - I'd say it was crucial, unless its moved to somewhere already waterlogged.

Okay let's return to Georgeb's original question which says 'more room for the roots' Looking at the photo I don't see anything that is going to hamper root growth Georgeb... if that is t he only reason you are considering moving I would definitely leave the trees where they are.

Muddywellies the trees may or may not survive moving. However, given that the trees are happy and growing well where they are I'd personally leave them be.