take some lessons, and then do the MSF course and pass it with a good understanding of the fundamentals, so that your parents can feel assured that you at least have the basics under your hat/belt. and so that you also have the confidence and knowledge not to drive your brand new bike into a tree like this:
http://www.youtube.com/watch?v=et0B-7gVTHU
but basically you need to be 10 times more aware of your surroundings and of what your doing compared to driving a car. cos a small bump, or swerve in a car might not be a big deal, but on a bike, it could mean serious injuries or even death.
ive come off my bikes a lot (and thankfully never seriously injured myself), and just last week end i was reminded how easy it is to get caught on the short end of the stick, when some idiot on a scooter was overtaking a car on a blind corner. i didnt hit her, but i dropped the bike where i stopped, because the curb of the road was washed out and it was about half a foot lower than the asphalt... no injuries, and no damage to the bike (miraculously) but it was a very close call.
basically you need the confidence to take the turns (turning stiffly is bad), be able to break fast, etc. but don't get reckless, thinking that you know it all after just 15k miles, because even when your not reckless, its easy to get in trouble.
ive been driving a bike in a crazy bike country for the past 10 or 11 years now, and im still learning how to take corners... and i don't think ill ever learn how to do it really properly until i get a chance to learn on a race track. specially since roads are so congested here, and all too often quite broken down.