A cello is too large to hold in your lap like a violin but far too valuable to trust to a moving truck, which puts it in an odd middle category: it needs its own seat, buckled upright, in whatever vehicle you are driving yourself.
Pro tip: If you do not own a second seatbelt-friendly spot, a cargo strap looped through the case handle and cinched to a tie-down point works nearly as well as a seatbelt for keeping it upright.
Watch out: Never leave a cello in a parked car, even for a short errand stop during a move; interior car temperatures swing far more extremely than the outside air and can damage the wood and varnish quickly.