The best way that it was explained to me, and trust me I'm still working a whole lot on it is this:
Completely separate yourself from the process and trust in the fundamentals. In bullseye it's focusing on each and every shot (which is completely exhausting), in USPSA it's on your plan.
Don't think about others watching you because chances are they don't care, they're more worried about where they place and their plan , and chances are they will forget about it by the next day. Don't dwell on the last shot, it's already gone.
It's all about the process, focus on that.