There is no bridge to Ocracoke. The island is accessible only by ferry.
From Hatteras — the most convenient option. The North Carolina Department of Transportation runs a free vehicle ferry from Hatteras to Ocracoke year-round. The crossing takes about an hour. No reservations — it is first-come, first-served. Ferries depart frequently in summer (roughly every 30 minutes at peak times) and less often in winter. In high season, expect waits of an hour or more for your vehicle to board; walk-ons are prioritized.
From Cedar Island — a toll ferry operated by NCDOT across Pamlico Sound, about 2 hours 15 minutes. Reservations are strongly recommended in summer and essential on summer weekends. Book well in advance at the NCDOT ferry website.
From Swan Quarter — another toll ferry, similar crossing time to Cedar Island, also requiring reservations in season.
The Hatteras route is the default for most visitors coming from the north. Cedar Island and Swan Quarter are useful if you are traveling from the south and west and want to avoid backtracking up the Outer Banks.