Wilderness State Park transportation to Mackinaw City?

You might try the ferry companies. I'm not sure about the State Park. But, our experience there was they run shuttles all over. Even take your bikes. All for free. As we were told' "We just haul you. Once you get to the dock there is no law that says you have to ride a ferry." You can use them to take you and your bikes into town and explore the fort and lighthouse museum from there. Then catch the shuttle back to the campground. JMTCW.