I have a Home tanning bed that I will need to install a breaker, wiring and receptacle. The bed is 20 amp 250 volt. Will 12/2 wiring be all right? Also do I need a double pole breaker for the fuse box, and if so how many amps?

Can you provide the nameplate volts, amps and/or wattage?

This bed was bought used and I can't find any plates on it. The plug (three prong) has 20A, 250 v on it. That's all I know

OK, then it should be safe to assume that a 20 amp 240 volt circuit will be sufficient.

This will need the #12-2 with ground cable , as you mentioned, and a 2 pole 20 amp 240 volt circuit breaker to match your panel.

You will need to match up the receptacle to the plug you have, which should be a NEMA 6-20P, as seen in photo.

I thought on a 2 pole breaker you need two hots, 1 neutral and 1 ground

I thought on a 2 pole breaker you need two hots, 1 neutral and 1 ground
The breaker is irrelevant.
A 240v circuit requires two hots and a ground. NO neutral is required or needed for a straight 240v circuit.

A 120/240v circuit requires two hots, neutral and ground. Some people call this a "4-wire" 240v circuit, but 120/240v is the accurate term.