With the UR12 interface unplugged from your PC or Mac, did you install a USB driver from Yamaha made for the UR12?
What happens when you plug in the interface? Does the operating system give any messages indicating it recognizes the new hardware?
Check your audio device list and make sure the device appears. Make sure it appears as a Recording and Playback device AND that it's enabled in both places.I have my audio interface set as my Default Playback and Recording device. Whenever it's not plugged in, Windows default to the internal audio ports (as long as they've not been Disabled).
ANOMALY: Some manufacturers expect the device to be using the exact same USB port every time, and plugging in to a different port causes issues for some devices. Must be an issue with their USB driver. Weird anomaly, I know, but it does exist for some hardware.
Bottom line, I do believe your problem is a USB connection issue between the Yamaha UR12 and your operating system. Get that remedied and Studio One should be able to use it.
Hope that helps!