should I plane down the stationary pad, or what?
I don't think so, but,
you are not giving us enough information to help you.
Did it drag before you left the driveway?
What kind of pads did you use?
Did it do this before you changed the pads?
I notice that this is "second" ride, when did you change the pads? Before the first ride or before the second ride?
What happens if you open (then close) the bleeder valve on the caliper to relieve the pressure in the system?
Did you meticulously clean the master cylinder and double check that the return port is clear?
Make that triple check the return port!!
More information please, so that we can help!