Best=convenience, price, time, etc. Must one go through Paris? Are there any bus options?
Pretty much all trains in that area (between Belgium and Normandy) go through Paris and it's a bit over 6 hrs between Bruges and Bayeux. Unfortunately there aren't many other options. You could rent a car but won't save either much time or $$. If you rent in Belgium and drop in France you'll most likely have a large drop charge. If you take a train to Lille and then rent a car you'll not save any time. This would only make sense if you plan to have a car once you're in Bayeux. I've not seen any buses that go directly between the two either.
That trip is not especially difficult, but it's going to take at least six hours. To answer your question, YES, you will have to go through Paris.
You could use a departure from Bruges at 08:08, arriving Bayeux at 14:19 (time 6H:11M, 2 changes at Bruxelles-Midi and Gare du Nord). That route requires passengers to make the trip from Gare du Nord to Gare St. Lazare via Metro or RER, and allows 50 minutes for that connection. I'd probably use the RER "E" from Magenta (which you can walk to from Gare du Nord) to Hausmann-St.-Lazare. When you arrive there, walk to the St. Lazare part of the station, which is where the trains to Normandy depart from. You can check all the rail solutions on the bahn.de website, and if you want to pre-purchase some of the tickets try the www.capitainetrain.com website.
According to Rome2Rio.com, no bus options.
In my perception of 'best', I would go with the option of renting a car at the Lille train station. While it won't save time, and will likely be more pricey, you could see the Amiens and Rouen Cathedrals on the way, drive over the Seine on that big bridge, have lunch in Honfleur, and have a pleasant drive along the coast before arriving in Bayeux at optimal check-in time.
After that, you'd have a car at the ready to drive on toward Mont St. Michele, Brittany, or the Loire Valley.
Thanks for your input. I asked the question for a friend; your responses confirmed what I had told him. Thanks again.