Buck Island itself has a 1.8 mile loop trail.
As noted above, the Buck Island Hiking Trail (also known as Diedrichs Trail) is a loop. The full route extends just 1.8 miles, though it's fairly steep on the way up. You'll want to allot yourself a minimum of 45 minutes for this adventure; a bit longer if you're keen on birdwatching or catching vibes along the more shaded portion of the trail on the north side.