Negative bar support has recently been added to Androidplot 0.6.2; you'll need to use the latest development version to get it (it's very stable).
Once you have the correct version of Androidplot you can use Maria Reina's suggestion to enable the display of negative values. Here's how I'm doing it in the screenshot below:
plot.setUserRangeOrigin(0);
plot.setRangeBoundaries(0, BoundaryMode.AUTO, 0,BoundaryMode.AUTO);

Note : There is currently a bug where if you are using overlay mode with 2 or more series and have negative bars, the overlay order of negative bars is reversed, causing the smaller negative values in a bargroup to be obscured by the larger ones. If your goal is simply to reproduce the image above though then you should be fine.