Keukenhof (in the rain?)

First of all, it isn’t dangerous to bike in the rain. Dutch people still bike to school and work when it rains. They put on rain gear and off they go. Biking through a thunderstorm is a different matter, this can be dangerous.
If you have your heart set on biking through the tulip area, I would always reserve bikes in advance.

We have tickets for the gardens and bike rental in May. We always travel with a rain jacket and depending on location and temperature rain pants. We also usually pack a couple of dollar store type rain ponchos. Don’t let the potential for rain ruin your day. When booking tickets you will see how many bikes are available for rent, they likely won’t be available day of. If you book bikes and the weather is truly awful, and decide not to use the bikes you will not be out a huge amount of money.

Sometimes tourists have to go to attractions in the rain. At least most of the paths in Keukenhof are hard-paved, and you can use an umbrella, because the trees shelter the wind to a great extent. You'd be worse off if you had to ascend a mountain for the view, and it happened to be a foggy day! Perhaps the usual Times-Square crowding at Keukenhof will be a bit better.

I personally don't find biking in the rain a pleasure. Be careful with raincoats catching in the chain, especially since chain guards are now considered hopelessly declassée. We were happy to look over the fences of Keukenhof, on the side where you can see some bulb fields in the near distance, from the comfort of your umbrella. Note that there are a lot of beer taps at Keukenhof. Whether they have bischopswijn, I don't remember.