Point out to your parents that lots of kids your age travel that far from home by themselves by car or transit. The fact that you will be on a bike is of no significance; cars break down all the time and kids miss their buses. Explain that you have a plan for every contingency. Show them that you know how to fix a flat tire, if you haven't already.
In a little over a year you'd be old enough to be fighting in a war overseas, or living independently anywhere you want. A self-supported bike ride seems like a very appropriate step in personal growth at your age.