From my experience girls in the dog park usally go there because ...
1. They have plenty of time (otherwise they would just take a short walk?)
2. Their bored and wan't to talk to people
3. Wan't their dog to have fun
Also they feel kinda safe there; and it's not odd if someone talks to them. Story telling is perfect DHV, try find out how she's training the dog. Most owners do train the dog to skip having it eating their shoes ... or even sofa if it's a big one:). Most people skip to answer 'Not training my dog' since it's kinda similar to DLV in dog park. That means she most likely replies with one of the answers bellow (and since you know the answer you can prepare for the follow up.)
* Agility
* Search
* Guard
* Rapport
Bonus, bullet proof way to get girls to stop you when taking your dog for a walk:
https://www.dropbox.com/s/kggz0zvu2jto825/IMG_1706.JPG