Cedar elm is very capable of being barerooted at collection. I've collected a few and ALWAYS bare root them--bacteria is NOT the reason. It is that native soil (usually fine sugar sand and clay) clogs drainage. You want very good drainage with a newly collected tree.
Bare rooting them doesn't really affect them all that much. If they're in reasonable bonsai quality soil, it's not a problem.
You can be very aggressive with root and top pruning with this species. I collect by measuring out from the trunk about eight or nine inches, digging down, severing all the roots in that diameter, then undercutting about three inches down. I trunk chop at the same time. Plant the new trunk in a pot that closely fits the remaining root mass and fill with regular bonsai soil. I have kept them frost free and moist as they recover.
Wait for new buds, depending on the age and thickness of the bark this can take a month or even two to show.
Don't worry about mycorrhiza. I don't think this species needs it, or even has it at collection. If it needs it, the approprirate species of myc (myc is species-specific, what works for pine may not be valuable for an elm) will return naturally.