Haarlem biking!

In late April this year, I stayed in Haarlem and took the bus to Keukenhof gardens. Haarlem is close enough to ride your bikes I feel sure but you will want to find out about parking your bike. Sorry my information is not definitive for your question. Everyone in Haarlem seems to have a bike though, as well as Holland in general.

Yes it is close enough and we've done it as part of a self-guided tour that passed by Keukenhof . Easy, pleasant, safe biking. Drivers of autos are very courteous. Advice: secure a map or directions. Enjoy.

The tulip fields are around Hillegom and Lisse, some 10 to 15 km from Haarlem.
Haarlem has at least two bicycle rentals: one at the station itself and Rent a Bike one nearby.

you are probably aware of the aalsmeer flower auction? when we stayed in Haarlem we got up early one morning and did the self guided tour of the auction complex. fantastic to see soo many flowers and activity.
hope this helps.

Thank you so much for your prompt response! We look forward to visiting the tulip fields in May 2019.

Reserve your bikes but check the bus schedules also. I'd still go to the gardens in the rain but I wouldn't want to ride there in it.

If you are going in May, make sure it is before the 19th. That's the last day in 2019.

If you are too tired to ride all the way back to Haarlem (not too far, but it does take a little while), you can ride to a nearby station and take your bike with you on the train after you buy it a ticket.