Amy, there should be a park ranger monitoring the entrance. You can buy a daily pass from them. However, on the chance that someone is not there, I'd suggest parking at the school.

If the ranger were to come back and you were parked in the lot, you'd probably get ticketed.

Or, if no ranger is located at the Bark Park entrance, I believe you could go to the Orion Oaks park entrance and get a day pass there. (Never been there myself... I believe the entrance is off of Clarkston Rd.)

Potato salad sounds yummy!