((not sure unsatisfactory conditions induce swarming, as opposed to absconding. In my experience, swarming occurs when hives are 'doubling'.))
You can easily move nearly a meter a day with no special efforts, if you keep the same entrance orientation. Some bees will overshoot, but will find their way back to the entrance. Swarmed hives are in the middle of a rapid hatch and those new bees will be orienting to the hive anyway-- leading to hover flights in front of the entrance that advertises its location.
It is easier to move "backwards" than forwards. Pulling a colony backwards, so the bees have to extend their landing flight, you can move 2 meters or so. Some bees will land early and walk to the entrance, so make sure they have a board or cloth runway.
You can successfully move an arbitrary distance if you loosely stuff the entrance with dry grass and cut and place a leafy branch in front and leaning on the hive. The process of digging out of the entrance and climbing through the branch reorients the bees (mostly). I make my moves at dusk or dawn when the hive is quiet. I've never thoroughly blocked the entrance with screen, but always used loose dry cut straw. I spray the hive entrance with essential oil-sugar mix, so the hive has a strong odor, and the bees are busy cleaning their porch of its traces. I don't know if that step is important, but it makes me feel like I am helping the process. I always smoke the hive on moves, I think the bees may instinctually reorient after a heavy smoking (don't know, and this might be magical belief).
I put a cardboard box a the old hive location to collect the insistent stragglers. The first night you might have 200 bees, that you can shake into the hive in the morning. The second night no more than 20. I don't use supers or formal hives, don't want the bees thinking their is a "hive" at the old location, just a refuge to keep them alive overnight.
I've searched for commentary discussing the number of lost bees in migratory moves-- haven't seen any, but I suspect that migratory moves have some significant impacts due to lost bees. Gypsy bees will move into any available hive (by report, I don't have independent verification).