From the Free Play portion of my Walk-through Comments thread (unrelated parts edited out):

Run left.
...
Stand on the brown square. Place the wheel and gold bell on the tricycle where indicated, then assemble the trike.
...
Hop on the trike and ride near the dragon while ringing the bell constantly. When the dragon spreads its wing around its head, immediately ride towards the door indicated by the new trail of studs (keep ringing the bell). As soon as the trike hits an invisible barrier, leap off and run through the door on the right. If you die, repeat this paragraph until you succeed.

Then solve the next room before returning to the dragon.
Hope your PSP is insured ;)