Hmmm... 15 minutes in the saddle is not long, as you stated. That kind of leaves me feeling suspicious that something else is going on.
Someone recommeded a while back that you may want to consider seeing a doctor just to make sure this isn't medically related first. From there, if the doctor sees nothing out of the ordinary, I'd consider your saddle- a better saddle could do wonders. In addition, a good bike fit would probably help you to correct your form so you are seated correctly (pelvis in the correct alignment on the saddle, sitting on your "sit" bones, etc.). I'd call around and see if you can find a good bike shop that can give you a thorough bike fit. From there, if you're still feeling discomfort, get padded shorts. If you're STILL feeling discomfort after all these preventative measures, consider buying a new saddle.
It also just may be that it will take time to get used to being on the bike and staying seated in the saddle.
Personally, I couldn't stand sitting in the saddle more than a couple of hours at a time. New shorts didn't do anything for me. I took my bike in and tried a new saddle, and the difference is like night and day. I can now sit in the saddle for hours and hours on end with very little shifting around.
Good luck, keep us updated with what you do.
Koffee