I also sometimes end up replanting herbaceous perennials with their roots bare, or just about bare. Examples that come to mind: brunnera (after taking out a bit of the plant which has reverted back to all-green leaf) or lungwort (when pulling apart what was several seedlings in order to keep only one).
I simply replant in well-prepared soil, pack the soil down (with hands or foot) and then don't let the soil dry out until the plant doesn't noticeably wilt when conditions get dry.
Have also certainly replanted shrubs with roots bare or relatively bare as well. Am assuming that spreading out roots can be a very desirable thing from several points of view.