Day train trip from London

Physically possible, yes. A pleasurable day? Not in my opinion.

There is more than enough in Bath to keep you occupied for a full day, allowing for the 2 hour train journey in each direction plus the journey to get from your hotel to the rail station.

London to Windsor by train will be c 1.5 hours from your hotel. Three hours minimum to look round Windsor. Windsor to Bath involves 3 trains and takes c 2 hours. Allow 2.5 - 3 hours to get back to your hotel from Bath and work out how long you would get in Bath, depending on how long a day you want.

Some coach trips cover both in a day for those that want a quick visit to each, but I don’t find that they give you long enough in each place.

Possible, but probably not a good idea. Bath is worth at least a full day. Windsor half a day, plus you have travelling time.

Train route: London Paddington - Slough (change) - Windsor & Eton Central
London Paddington - Bath (no changes)
But to get from Windsor to Bath involves 2 changes: Windsor & Eton Central - Slough (change) - Reading (change) - Bath
Trains to Bath go through Slough, but don't stop there, first stop out of London is Reading. Hence the double change.

Thank you for the good advice. We will limit this day trip to Winsor.

As Chris said take train from Paddington Station, when you get to Windsor as you exit the train turn right and walk up to to High Street, you will see the castle across the street.