It will never get to exactly zero as there is a voltage drop across the transistor, \$V_{CE}\$\$V_{CE_{(sat)}}\$ which can be several tenths of a volt with a bipolar transistor. A MOSFET might get you closer or you could use a negative bias to offset the output. You might also be able to put a diode in series to drop the output voltage a bit.
Another option is to add a PNP transistor, this places the \$V_{CE}\$\$V_{CE_{(sat)}}\$ drop at the top of the waveform instead of the bottom, so you'll lose a few millivolts on the high part but get much closer to zero on the low part.