An orchid's bloom spike is the single most fragile part of the plant to move; it snaps far more easily than the leaves or roots. Staking the spike and cushioning the blooms in tissue is the whole job.
Pro tip: If the orchid is in full bloom and the move is long, it is fine to snip the spike above a node instead of risking it snapping; it will rebloom later.
Watch out: A blooming spike is brittle and snaps easily if bumped or pressed; always transport orchids upright and unstacked.