Short answer: a local hot tub move typically costs $300–$800 with the right crew and equipment. Added to a long-distance household shipment, it usually adds a flat $300–$450 rather than pricing by mileage.
What you handle vs. what the movers handle
Draining the tub, disconnecting the electrical hookup (often a job for a licensed electrician if it's hardwired), disconnecting any plumbing, and removing the cover and skirt panels typically falls on you before movers arrive — none of that is part of the moving quote itself. What you're paying for is safely lifting, transporting, and placing the empty shell.
Full-service crew vs. hot-tub specialist
Many full-service moving crews can handle a standard rectangular or round hot tub with a proper dolly and enough hands, provided access (doorways, stairs, yard gates) is reasonable. Oddly shaped tubs, rooftop or elevated placements, or very tight access points are where it's worth asking specifically whether the crew has hot-tub experience or whether you need a dedicated specialty mover.
Getting it into your full move estimate
If you're already comparing full-service moving quotes, flag the hot tub at the start — it's one of the checkboxes in the calculator above — so every quote you get already accounts for the extra crew and equipment instead of showing up as a surprise line item after booking.