Feeling fear is a sign of progress not a sign of weakness. So, it's okay to feel fear while we are confronting the bully. What we do NOT want to do is avoid the fear in order to stay calm.
From the book: Confronting the Bully of OCD
Note: Practice with one small fear, not a big one. Pick something avoided due to fear, (like not riding a bus, walking on cracks, or whatever it is that makes you fearful but is on the bottom of the list in order of fears.
OR try not to do a particular compulsion (if that's your issue) that is done out of fear thinking that something bad will happen unless it's completed. Maybe not counting things, leaving a picture crooked on the wall, not checking the stove or plugs, not washing hands so often...there are so many, it doesn't matter what it is. Just try not doing it for an hour, then maybe a couple hours. Don't listen to the OCD bully's threats.