Keukenhof is opened from mid-March to mid-May (check the website for detailed dates). Best date visit is begin-April to mid-May as not a lot of flowers are in bloom during the first weeks. It starts out with more basic flower bulbs beginning of the season. Mid-April the trees are also begin to bloom (just something extra).
If your oke with not seeing everything of the park in one day I suggest you go early in the morning or late in the afternoon. Between 10:00 and 16:00 it is the busiest time and the park will overflow with visitors. You can better enjoy the park with less people in it ;-).