This only happened to me once. It was a monster and by the time I realized I wouldn't be able to clip out, it was too late. The fear of falling got me over to top. Relax (drop shoulders), breath (seriously), pedal. Repeat.

Just get out there and do it. My fear used to be riding on the road and being hit from behind. I learned: 1) that's not the most common accident 2) take the lane instead of hugging the curb 3) Longer distances would only be possible if I took to the road