By train: Bayeux is on the Paris–Cherbourg line. There are direct TER trains from Caen (20 minutes, frequent), and from Caen you can connect to Paris Saint-Lazare (2 hours). There are also some direct trains from Paris Montparnasse to Bayeux, though Caen is the more frequent interchange.
By car: From Caen, take the A13 autoroute west and then the N13 to Bayeux — about 30 km. From Paris, take the A13 to Caen and continue on the N13, total around 3 hours.
From the UK: The most direct route from Britain is the ferry from Portsmouth to Caen (operated by Brittany Ferries, around 6 hours) or Portsmouth to Le Havre, then drive west to Bayeux.