I have a patch of them next to a gravel path, and they reseed into the gravel constantly. I move some of the seedlings each spring before they go dormant, and I can still find them; and never have had a problem getting them to live. They have a taproot that looks like a carrot. The big ones are hard to move, but the babies are never a problem. Just dig them up and put them where you want them, and forget them. They do like lots of light tho not direct sun, and don't need any special care. It is a good idea to mark where you've put them so you don't accidently dig them up or plant something on top of them, tho I did inadvertantly plant a hosta in the middle of one patch. Both plants are fine, and the bluebells came up anyway. I'm sure they are putting lots of seed out for you, but it may not germinate due to good weeding or cultivating practices. The seed falls into the gravel path here and doesn't get dislodged before it germinates. It does take 2 or 3 years for the babies grow up big enough to bloom, and they are easily mistaken for weeds until then. It's kind of a myth that they need rich woodland soil and lots of moisture. They do like average woodland soil, and moisture in the spring when they are growing, but when they are dormant average rainfall is fine. They even survive a drought without a problem. Sandy

They can be moved while in bloom. During a gentle rain or on a cloudy day early morning or late afternoon. If they are mature plants they will have an extensive root system.

Even if the flowers and foliage wilt upon transplant - which is very likely - I would venture to say that, if the bulb sections are big enough, they will sprout again the following year. This is an extremely vigorous plant which will spread extensively once it gets started. I compost a goodly amount of it every spring just to keep it in check, yet I'm still inundated by it (in a good way ... sort of). If you wait too long in the spring to transplant, the above ground foliage will disappear and be difficult to find. I would wait until the flowers start to fade and do the transplant then. The foliage will probably wilt but the plants should grow and flower fine the next year. This is actually a very difficult plant to get rid of once you have it, lol.

I would transplant in the fall. The roots might get damaged if they stayed in the pots all winter.