Dog Park

We took Bauer to the off-leash park yesterday and today. At first he was very tentative and hung out between our legs for a while. Then he met a cute little dog, about his age and size and had a wonderful time. When we went back on Friday, little Ella was there again and the two of them rip-roared around the park.So going to the dog park, we realized quickly that no one introduces themselves, it's just the dog that gets the introduction? We met a nice couple there on Friday however we only know their dog's name, Charlotte. When is it proper to introduce yourself? 2nd, 3rd meeting? Or is that just not done? I'll have to rent Dog park again and see what the etiquette is.
Bauer was so tuckered out, he could hardly keep his eyes open on the short ride home.