What is the fastest way to get from AMS to Kerkenhof Gardens?

I don't have an answer, but highly suggest your travel plans allow you to arrive as soon as the gates open. It's the least crowded part of the day. The gardens are amazing. Enjoy!

There are direct buses from both Leiden and Amsterdam to Keukenhof. On the Keukenhof website, buy a combi-ticket to the gardens. This includes transportation both ways as well as discounted garden tickets. It's all explained on the Keukenhof website. If you fly into Amsterdam, you can even go from Schiphol airport to Keukenhof on a special bus, taking your luggage with you and storing it at the gardens while you visit.

If you are referring to Schipol airport (whose designation is AMS),
You can catch the Keukenhof bus from the airport.
Go to their website and buy a combo bus/ticket.
When you exit Schipol plaza, turn right, walk about 300-400 feet til the building ends and turn right .and the bus line to Keukenhof will be there.
There will be Keukenhof employees there to help you, check your tickets and direct you to the line for the bus.

While there are other pickup points in the central Amsterdam area for the combo bus/ticket , we took the train to Schipol, and then the direct Keukenhof bus from the airport. Easy peasy.

Just wanted to add, that if you get the Keukenhof public transit combiticket originating in Haarlem or AMS, you can use that to take the bus to Leiden afterwards. They're all lined up outside the park & it's super easy to navigate. Last spring, I took the first bus from Haarlem, spent the morning/lunchtime at Keukenhof & then spent the afternoon/early evening in Leiden, then train back to Haarlem after an early canal-side dinner. It was such a wonderful day & probably one of my favorite day of the trip! Pro tip: take a canal tour when you get to Leiden...great way to get your bearings, plus it's nice to sit down after walking around the gardens all day.

It sounds like you are going to be encumbered by luggage, if you are starting at AMS? I wonder if you are assuming that it is easier to get to Keukenhof from the airport than from Amsterdam, after you check in (or leave your bags) at your hotel?

It is ambitious to plan Leiden along with Keukenhof on the same day, because Leiden cannot be "done" in a full day on its own. But it's your trip. And you have to add in those public transit runs, which require wating for a bus, as well as making stops along the way if it's a regular public bus.