Bus from Amboise, France to Chenonceau Chateau

Take the train instead or take the bus there and the train back since the train runs all day.

For what it’s worth, we rented bicycles in Amboise and rode to and from Chenonceau. The pedaling was pretty flat (not completely), the route finding was very easy, and it didn’t take too long by bike. A great day, in all.

According to Rome2rio you need to catch bus C from: Théâtre Beaumarchais, Av. des Martyrs de la Résistance, 37400 Amboise, France and stand on the east side of the street on Av. Des Martyrs de la Résistance (30m). I did this in 2012 but don’t remember the street name so I also suggest asking a local i.e., your hotelier or host.
You will get off at CentreSaint-Georges-sur-Che and walk to: Château de Chenonceau, 37150 Chenonceaux, France (15m). This is an easy walk and you will not be alone just, follow the crowd.
I don't see trains that depart in the morning. The bus is faster too.

There's a new shuttle bus service been announced. The only info I can find so far is this : https://www.remi-centrevaldeloire.fr/tourisme/navette-chateaux/

It may be worth emailing the Tourist Office in Amboise.

Although the train looks like an attractive alternative, it's too complicated, and usually involves a long connection at Saint Pierre des Corps.

You can't prebuy tickets on the regular bus, but if you're at the first bus stop on the rote 10 minutes before the bus goes you'll have no problems. Usually the bus is nowhere near full.

I posted about the Sunday Shuttle between Amboise and Chenonceaux (also operated by the public transit provider) after I took it a couple of weeks ago:

https://community.ricksteves.com/travel-forum/france/new-trial-sunday-shuttle-service-between-amboise-and-chenonceaux-through-july-2

I have also taken the regular bus from in front of the theater, around the corner from the post office. It is mainly school kids going to the area high school that is a bit outside town. After that you have the bus to yourself.

The walk from the regular bus to the Chateau is not long at all.

The shuttle bus on Sundays literally drops you in the chateau parking lot.

Here is another secret: the time on your chateau ticket these days is literally the time you go into the Chateau itself. You can enter the grounds at any time.

So in other words if you purchase a 10:45 Chateau ticket, you have to get from the bus stop to the Chateau grounds entry, and walk the rest of the distance to the Chateau to enter the Chateau itseld by 10:45. If however you bought say an 11:30 ticket, you could still enter the grounds as soon as you got to the site, but you would be able to look around the grounds until heading to the Chateau itself for 11:30. (I am not saying this is what you should do, just explaining how they have changed the tickets a bit recently.)

I am not sure a couple of hours would be enough for me to see everything if it were my first time there, but I really like the gardens. You could definitely see the Chateau itself and get a glance at one of the gardens in two hours.

Thank you for these wonderful responses so far! Mary Pat, Simon, and Kim you have given me some great ideas to consider. It is very helpful to get everyone's perspective.