You should get a RAM mount. I have a Garmin eTrex mounted to my Fuji's handlebar using a RAM mount that I used to use on my motorcycle.
They're available from a number of places, but in my experience GPSCity.com has the best prices.
iPhone 3/3GS mount:
http://www.gpscity.com/ram-mount-app...149z-ap9u.html
iPhone4 mount:
http://www.gpscity.com/ram-mount-app...149z-ap9u.html
If you Google around you can typically score a 5 or 10% off coupon too. Google "gpscity.com +coupon"