Is there enough time to find and board the trains with a baby?
Yes, no problem. Be sure to be on the platform waiting.
Separately do we sit anywhere or do we have assigned seats?
When you buy the tickets, you will be offered reserved seats on the train(s) that have them
1) Windsor to Slough - This is just a shuttle train, no reservations.
2) Slough to Reading - not sure if reserved seats are an option on this train.
3) Reading to Bath - this is the train from London to Bath, first stop Reading. This will have reserved seats as an option.
Are bathrooms available on the train?
Bathrooms never (It is a standing joke that US-Americans call a toilet a bathroom. A bathroom is a room with a bath in it!)
Toilets: (1) No, but it is only a 6 minute trip. (2) Possibly (23 minute trip). (3) Certainly (60 minutes).