Luggage

Check to see if they have a coat room/cloak room that will store your luggage while you are touring the castle. Many places don't want people bringing in umbrellas and rain coats.

To get into Windsor Castle, you go through airport-type screening, and large bags etc. can't be brought in. They have to be checked, along with other prohibited items like knives etc. See the website. I haven't done this but I'm sure you won't be the first.

I'd recommend the train for a faster, more comfortable trip. You want the Eton & Slough (rhymes with cow) station, where a short spur line runs often to the station called "Windsor & Eton Central." The other station in Windsor is farther from the castle and, I think, also not as easy a connection from Bath.

This doesn’t answer your question, but Windsor might be better done as a day trip from London rather than messing around with buses.

Bath to London is a straightforward train trip (90 minutes). Windsor is a very straightforward day trip from London. Unless you have a car, it really is much easier doing it that way than struggling with the hassle of luggage, buses etc. I know it looks like Windsor is en route to London from Bath but really it isn’t in terms of train routes.

Luggage lockers/left luggage disappeared from most train stations in the UK when IRA terrorism was a real danger. Some big stations -for example in London and major cities - have expensive left luggage with airport-style security.

According to the Windsor Castle website they do have a cloakroom where large bags can be left. This is what it says:

Cloakroom facilities

There is a secure cloakroom in the China Museum at the entrance to the
State Apartments for the storage of large items of baggage. Large
backpacks and pushchairs are not permitted in the State Apartments and
must be checked in here.

There is no limit on the size or weight of luggage brought into the
Castle cloakroom. However please bear in mind:

the walk from the Admission Centre to the Cloakroom takes about 10
minutes and is uphill to begin with, although it flattens out along
the route. there is a flight of stairs to negotiate once you arrive at
the entrance to the State Apartments. your luggage will need to fit
through the airport-style security scanners in the Admission Centre
before it can be brought in to the Castle. If you are planning to
visit Windsor Castle on your way to/from the airport you might find it
easier to use left luggage facilities at the airport or in central
London.

Thank you all for your replies. Much appreciated.

On the Windsor Castle website it says that some items such as large baggage, backbags etc., will be checked in and reclaimed at the end of the visit, I’ve never tried doing it, so not sure if it works well or not.