This is an odd thing to want to do. The efffort and cost to do this make just driving it in a car a better idea. It won't cost much less than shipping it across the country and you have to get a box and disassemble and pack the thing.

If it's a round trip for the rider and the bike, it's not clear why they just don't ride it both ways. While you might need to work up to 60 miles, most reasonably-fit people can do that if it's not too hilly (though they might take some time doing it).

Your mountain bike doesn't weigh 20 pounds.