Cannot Google answers to these questions

If you request a train schedule from Rotterdam to Bayeux, it will include adequate transfer time between the stations, usually at least an hour. How to Look Up Train Schedules Online gives you the DB train schedule link and tips for using it. A bus outside the station would often be my first choice as a single traveler, but if you don't see one arriving, or if you have several people with luggage, then I would take a taxi.

The direct Paris-Bayeux train around 16:00 on Sundays looks like your best choice. I expect the Caen train station to be pretty small and manageable, with quite a few people making the same connection, if you have to take a later train.

aspiring,

The first part of that journey is straight forward. This is probably the route I'd follow in the same situation.....

• Travel via Thalys or whatever from Rotterdam to Gare du Nord. Travel time will be ~2H:37M.
• Walk to Magenta station.
• Take RER "E" from Magenta to Hausmann St. Lazare.
• Walk through the station and upstairs to Gare St. Lazare (as I recall, there are Escalators).

Check the bahn.de website to determine times for trains from Gare St. Lazare to Bayeux on Sundays. You could (for example) use a train departing at 11:33, arriving at 14:15 (time 2H:42M, one change at Caen with an eight minute layover).

Getting a Taxi in Bayeux on a Sunday may be "hit & miss". There may be Taxi's waiting, but in the same situation and on a Sunday, I'd contact the hotel and pre-arrange a Taxi.

Happy travels!

Following up Ken’s good advice, here are some more tools:

www.thalys.com is where to buy the Rotterdam-Gare du Nord ticket. It is a beautiful train and the tickets are not cheap.

www.ratp.com is the key to mass transit in Paris. It has an interactive tool to show the route from Gare du Nord to Gare St-Lazare. Its estimate of the time required is optimistic if you need extra minutes to sort out the signs.
www.parisbytrain.com discusses train stations, with photos.

http://en.voyages-sncf.com/en/ is the SNCF site in English. It will sell you tickets. You will see four direct trains from St-Lazare to Bayeux, any day of the week. Changing trains in the small Caen station is easy so eight minutes should be enough and there is no seat reservation on the 15-minute run to Bayeux. Or you could taxi, for about 25-30 euros.
I am a fan of Caen and suggest spending a day there, particularly for its own WWII history, its ancient fortress, and the relatively new war (or “peace”) museum, which runs a Normandy beaches tour.

As always, the encyclopaedia of rail travel is www.seat61.com , both for schedule sources and ticket-buying tactics.

Thanks to you all for such intelligent and speedy responses. Indeed your collective knowledge is more helpful than Google!

I frequently need to get from the Gare du Nord to the Gare Saint Lazare. If I have lots of luggage, or if it is late in the evening, I take a taxi; it should take no more than 30 minutes, maximum. When I'm traveling light, I walk outside the Nord station and get the 43 bus, which stops at Saint Lazare. Her is a link to RATP, the Paris public transportation system:
http://www.ratp.fr/en/ratp/c_21879/visiting-paris/