Tilghman Island is about 90 minutes by car from Annapolis and Baltimore, and about two hours from Washington DC. Take Route 50 across the Bay Bridge and east to Easton, then Route 33 west to the island. The single drawbridge over Knapps Narrows is the only crossing; on busy summer weekends, occasional delays for boat traffic are part of the experience.
There is no public transport to Tilghman Island. A car is essential. If you are doing a broader Eastern Shore loop — Easton, St. Michaels, Oxford, Tilghman — allow at least two days.