Apple juice is a bladder irritant, which irritates the lining of the bladder, causing it to feel the need to empty more urgently.

You can read more about bladder irritants here:

http://www.healthcentral.com/incontinence/c/52/2715/you-eat/

http://www.healthcentral.com/incontinence/c/45/1870/caffeine/

Especially since you're so young, I'd certainly recommend that you see a urologist or urogynecologist about the episode so that they can perform some tests and rule out any serious causes. In the meantime, if you experience more leakaage, you may want to try an elimination diet. Simply cut any potential bladder irritants out of your diet (coffee - including decaf, chocolate, apples and apple juices, spicy foods, carbonated beverages, beverages with caffeine, and citric fruits and juices). Then add the foods back into your diet one at a time, one per week. If you start having a problem again, take the latest food back out of your diet again to see if it gets better (keep going back up the list taking foods back out of your diet one at a time until you figure out the culprit). After you figure out which food was causing a problem, keep adding any remaning foods back in one at a time (often you'll be sensitive to more than one food or category).

Hope this helps, but do make sure you see a doctor!