The website of the Exmoor National Park Authority (ENPA; www.exmoor-nationalpark.gov.uk) lists some of the moor's key bus services (under Enjoying/Travel). Be aware: some are seasonal, and the more remote services are particularly prone to change.
Bus 28 Shuttles from Taunton to the resort of Minehead (£10, 1¼ hours, at least hourly).
Bus 300 A vintage bus which runs between Minehead and Lynmouth (£10, 55 minutes), via Porlock (£6, 15 minutes). The service is limited to two buses daily between Monday and Friday, from mid-July to early September only.
Bus 309/310 Runs from Barnstaple via Parracombe to Lynton or Lynmouth (£3.60, one hour, hourly Monday to Saturday).
Bus 198 Runs between Minehead and Dulverton (£4, one hour, two to three daily Monday to Saturday), via Dunster (£2) and Wheddon Cross (£2.70).