You train to ingrain the fundamentals of shooting into your mind and body. It would be prudent to do the same thing with your first aid gear. You do not want to be figuring out how to apply a tourniquet (TQ) with one hand for the first time after you have a wounded arm.
This video from Tactical Medical Solutions, makers of the excellent SOF Tactical Tourniquet, explains how to avoid the pitfalls of unrealistic training for one handed TQ application. It also outlines a handful of ways to complete the application of a TQ using just one hand.
Check out the TacMedSolutions blog for tons of great first aid information.