Being a cheap skate, I usually park along side Sycamore Park (this address will find it for you 8246 E White Oak Ridge, Orange, CA 92869) and ride over.
The park has bathrooms if needed.
The downside it that it is 3/4 of a mile just to the dirt at the Irvine park entrance an then you still a mile and a half to Santiago Oaks proper.
An alternate (free) entrance is at 6517 E Mabury Ave. No bathrooms, but only a half mile along the Santiago Creek Trail to Oaks proper. The down side here is that it is on the wrong side of the park if you want to leave after coming down Chutes, resulting in a long detour back to your car.