Ideally the bulbs should be dug just as the foliage starts to yellow and die off in late spring, like when dividing daffodils (same family). Then they can be spread out to dry. After drying the leaves fall away easily and the bulbs can be stored in a dry place till fall when they can be re-planted. I use mesh onion bags and hang them in a garden shed.
If you have to move them while they're in active growth, I would recommend getting as much of a root ball as possible and gently placing them in a holding spot. Sometimes disturbing bulb plants while in active growth sets them back a year, but if there isn't too much root damage they should be okay.
