Sembach,
As previously mentioned, my daughter and I took a public bus from Amboise (across the street from Theater) to Chateau de Chenonceau, the bus stops in front of the castle gate.
I did a bit of research and found the bus that my daughter and I took from Amboise to Chenonceau castle.
If you plan to stay in Amboise, I'd urge you to go to the TI office as they were very helpful.
They will provide you with a map and will mark where the bus stop is located.
Here is the link to the bus https://www.remi-centrevaldeloire.fr/itineraire/
You can see the bus schedule by choosing your desired departure and arrival as follows:
- Départ: type Amboise and choose, "Théâtre (Amboise - 37)"
- Arrivee: type Chenonceau, and choose, ''Château de Chenonceau (Indre-et-Loire - )''
- choose desired date
- choose a time in the morning, say 8am
We took the bus "C" in Amboise at 9:53am and arrived to the castle stop at around 10:21. We then took the bus back to Amboise at around 12:20pm
Here is the bus schedule
The top schedule is the one you need for the return; Chateau de Chenonceau to Amboise (bus originates in Montrichard)
The bottom schedule is the one you need to go from Amboise to Chenonceau (bus originates in Tours)
Tocard already provided you with the link to the bus shuttle if you want to visit Chambord and Cheverly.
The location of this bus is a bit tricky as there was no signage when we were there.
When you exit the Blois train station, turn left and go past the parking lot and into another parking lot where you will see the shuttle buses parked.
If you decide to stay in Amboise, make sure you plan to eat a delicious meal at Chez Bruno (reservations required)
Hope this helps!
Edited to add:
I forgot to mention that the public bus (Amboise to Chenonceau) does not run on Sundays.