I have done the Fat Tire bike tour and it WAS really fun.. even though I had already been to Versailles at least half a dozen times before.
The palace is very crowded and hot.
Maybe consider a daytrip to Provins ( look it up , world heritage site) or Pierrfonds instead if just going for the "see a palace/castle" thing.. Provins doesn't have an actual castle but it has old medival ramparts, an old town, and shows that are worth seeing, I saw the Birds of Prey one and it was pretty cool,, they are outside and the participants are in medival costume.
Pierrefonds is a rebuild.. but its where they filmed parts of Merlin.. so kind of cool looking, and the little lake has some cute places to grab lunch .
I love the history of Versailles , but over the last 10 years its just become harder and harder to enjoy the palace.. its really a mosh pit, with no air conditioning.. and pushy tour groups. The grounds and outer buildings are still wonderful.
Personally I would avoid weekends.. the fountain show wasn't worth the etc crowds to me.. but I have been numerous times now so perhaps I don't see things the same way.
The bike tour was at request of a friend.. I was against it at first,, but I was wrong, it was a fun day.