Leave the car in Mackinaw City or St. Ignace. The island does not need it, and the crossing is the point of the trip. The bridge is the photograph, taken from the mainland. The ferry is the arrival.
Mackinac Island sits in the straits, not on the bridge. A single day is enough if the plan is Fort Mackinac, the shore road, and one meal that is not fudge. The fort is on the bluff above the town. The shore road is the level way around. You can walk both if you do not also try to collect every inland trail.
Rent a bicycle only if the weather is settled. Walk if the wind is up. Early October is past the thickest weeks, and the wind on the straits does not read the calendar. The quiet hour is late afternoon, after the day boats have turned back and before the lights on the bluff take over. This piece does not promise a particular boat or a fare.
Do not try to see the island and a second destination on the same afternoon. The color roads of the Upper Peninsula are a different day, and so is a full tour of both bridge towns. The straits are the destination. A rushed return across the bridge wastes the reason you came.
The town will sell fudge. That is a fact about the main street, not an instruction. Eat something that is a meal, walk to the fort wall, and take the boat you meant to take. The car will still be where you left it.