Asparagus doesn’t mind. You can move them in the Spring while they are still dormant (no spears poking up) as soon as the soil can be worked, or in the Fall after the green tops start dying back.
I would chose Spring over Fall, though. Our bed is pretty ratty - needs a major refresh, but I’m not looking forward to that task.
Here’s a pretty good primer on what to do:
https://www.asparagus-lover.com/transplanting-asparagus.html
Thanks for the asparagus link.
I’d hoped to get the rhubarb in after work yesterday but that little squall that blew in off the prairie had me tying things down instead of working in the garden. I’ll make another attempt this evening if the rain holds off.