A bonsai's value is in years of careful shaping, so the shallow pot and trained branches deserve more care than an ordinary houseplant. Rigid support and zero shifting room are what protect the trunk and canopy.
Pro tip: Photograph the tree from all four sides before the move so you can confirm no branches shifted or snapped in transit.
Watch out: A shallow bonsai pot tips easily; any box it rides in must hold the pot rigid, not just cushioned.