JuneJuly 2024 where to stay in B& B near Versaille and near metro into Paris
You are aware that the Olympic Games will take place in Paris in July 2024, right?
If you do not plan to attend, I would steer clear of Paris (including Versailles) for the whole duration of the games.
Otherwise, staying in Versailles for sightseeing in Paris is not super convenient. The metro does not reach Versailles: you have suburban trains instead, which are not that different but they are a bit less frequent and it will typically take 45-60 minutes to reach any given point in Paris from somewhere close to one of the Versailles train stations (there are three main ones and two small ones).
This explains why there is less accommodation in Versailles than one could expect.
With these caveats out of the way... I confess that I have no idea about Versailles B&Bs - as a Paris local I am not in the best position to recoplend hotels.