We went mid-April and perhaps about a third of the tulips were in bloom. I think that in the next few weeks it is going to get even more spectacular; so get yourself down there!
The best travel option for us was to go down the S2 to Gesundbrunnen Bahnhof, travel around the ring clockwise on the S41 to Hermannstraße, then catch the M44 bus (direction Stuthirtenweg) which in thirteen minutes stops just outside the entrance to the Britzer Garten. Or get off a stop before for the windmill.
Here are some photos of the day to tempt you.