I saw the gardens in the end of April, so this year's long winter worked in my favor. The outdoor areas were mostly still in bloom or just starting, but the indoor blooms were all breathtaking. I am not an outdoor person, nor someone with a green thumb (quite the opposite) but I thoroughly enjoyed the park. Even with an old digital point-n-shoot camera, came away some really nice pix.
The park also has great areas for kids with a petting zoo, picnic areas, and a windmill you can go inside. You can definitely spend an entire day in there without being bored.
Transport from Amsterdam is very easy. I stayed near Centraal Station, so opted for the Combi-Ticket from Schiphol (one easy train ride away). You can even get the combi-ticket at the TI across from the train station (bought mine the day before), if you did not order it online.