Ultimately, what you have "planned" will give way to what you "desire". An alcoholic does not go into a bar and sit among the people swigging down beer and buying rounds for the house. A young man with desires should not put himself into a position where he is likely to have the opportunity to act upon more natural instincts.
While your head says you will not allow it to go further, trust me on this - your hormones will over-rule your head and will take control at some point not too far down the road.
By allowing yourself to see her your feelings will get stronger for her, and your desire to do more than have stimulating conversation will grow. And I have my doubts as to just how stimulating a 15-year-old's conversation can really be ... again, unless your level of maturity and interest is below your age level.
You are heading down the road to disaster here.
The most likely code sections you might run afoul of are: PC 261.5 (stat rape), PC 272 (contributing to the delinquency of a minor), PC 647.6 (annoying/molesting a child), PC 288a (oral copulation with a minor).
Instead of looking at this from a legal point of view, you need to evaluate it from the moral one: is this a good idea? The fact that you question it tells you that you KNOW the answer already ... and it's "no".
You WILL become aroused ... you WILL find yourself drawn in to more than hand holding and conversation ... and you WILL get in trouble.
Also, I note that you asked her mom for permission, but you did not mention what she said.
- Carl