I'm the same way...worse even after crashing at the bottom of a hill. I did a race a while back and people were not happy with me on the downhills.
It takes time. Once you feel more confident/experienced, you'll relax a bit!
2007 Trek 5000
2009 Jamis Coda
1972 Schwinn Suburban
"I rejoice every time I see a woman ride by on a bike. It gives her a feeling of self-reliance and independence the moment she takes her seat; and away she goes, the picture of untrammelled womanhood."
Susan B. Anthony, 1896