I will only discuss, long distance movers that can move your hot tub. If you are looking for local guys you might as well, call some guys that can also install it for you.
Well moving a hot tub is like moving any other bulky item. If this is the only item you are planing to move make sure it is cost effective to move it. Call around, you are probably will have to spend more than $1,000 to move it depending on the size of the hot tub, and how far you are planing to move it. Check with a moving broker they sometimes will have great deals on back-loads. There are many sites that will provide you with a multiple quotes.
Here is the actual page for Hot Tub Movers on http://www.GotMovers.com
Good luck, and please feel free to comment.