We have contacted Mustang Island State park and got the following information:
There is a 1.5 mile stretch of beach for "primitive campsites". These campsites are for up to 8 people and are 8 dollars per campsite. Since we will likely have more than 8 people camping, we are allowed to set up "campsites" right next to each other. I explained to them that we will be on motorcycles and that was not a problem. The total fee's are 4 dollars per person and 8 dollars per campsite. There are convenience stations with toilets, rinsing showers and bulk water supply located in the primitive camping area. The gates to the park are locked after 10pm, however we will be provided with a code, in order to come and go as we please.
More info located here:
Mustang Island State Park
Directions: To reach the park, travel southeast from Corpus Christi on State Highway 358 to Padre Island; cross the JFK Causeway; continue one mile to traffic light; turn left onto State Highway 361 (used to be Park Road 53), and go 5 miles north to park headquarters for a total distance of about 22 miles. The physical address of the park is 17047 State Hwy 361.