30 amp rv receptacle installation
Your RV plug is a TT30.    The 10/3 NM "Romex" building cable is sufficient to the task provided it is not exposed to weather.  If exposed to wet or weather, you just need a different category of cable for the exposed run. 

You can use this with a 30A breaker, either single pole or double pole.  In either case you land the in-use hot wire (black preferred, red will also suffice) on one of the breaker poles.

The other hot wire, cap it off on both ends: put a wire-nut on it (probably yellow), tape that nut on (nuts don't like to stay on single wires), and tuck it back. 

If  you ever have call to fit a NEMA 14-30 receptacle out there (say, for a larger RV, which uses L14-30), it's now an easy job.  

You could also fit the NEMA L14-30R today by using a 2-pole breaker and both hots -- then this $20 adapter cable.  This is safe because it's a 30A-30A adapter, so properly breakered.