How to best see flowers and flower fields near Amsterdam April ‘22

You can get public transport from Schiphol airport or Amsterdam to Keukenof. I recommend arriving when they open because it will be a mob scene of tourists. https://keukenhof.nl/en/ov/

As for the fields, I took the train from Leiden to Haarlem after visiting Keukenof and was overwhelmed by vistas of tulip fields on both sides.

The easiest way to reach the Keukenhof is to go buy public transport. The Keukenhof website has all the information about what bus to take and about the bus/entry combo tickets; https://keukenhof.nl/en/ov/
The best way to explore see the tulip fields around the Keukenhof is by bike. Bikes can be rented near the entrance of the Keukenhof.
No matter how you explore the region, please don’t enter the tulip fields, not even when you see other tourists do it. The tulip fields are private property of the tulip farmers. People entering the fields can spread diseases and damage the plants.

I don't know if this would satisfy you, but while you are at Keukenhof, there are a couple of vistas over the perimeter fence (I mean, inside looking out) that reveal several nearby bulb fields, most likely in bloom. As noted earlier, you can't walk through them anyway, and they are down a steep hill, AFAIR. Try to go on a weekday in the hope of smaller crowds.

Serious cut-flower folks (well, I saw some potted shrubs being auctioned too) may wish to attend the early-morning commercial auction at Aalsmeer, but it's a big chunk out of your day, and harder by public transportation. They have a restaurant attached to the "Visitor Catwalk" that your visit is on. One reason for going is that this could possibly become a virtual event, although it has a physical presence tradition. You can see the bidders and their laptops as part of the visit.

Thanks for the relies… most helpful!