I have a tanning bed that has a 3 prong male plug - I need to wire an outlet with 20amp service - will I only need to run a 12/2 wire - using the white and black as hot??

Assuming you need 240 volts, then yes, you can use #12-2 cable with a black and a white (plus ground). The white needs to be identified at both ends and where exposed in any junction box as a hot conductor, usually with black electrical tape.