Is there a global database available for groundwater basins (Aquifers), similar to gdbd for surface water?
I don't believe these are 100% on target, but they look pretty promising.
I can't post more than two links yet, but the USGS has a pretty solid database for all bodies of water in the United States, so make sure to check them out for US based data, at least.
Global Water Forum lists a number of water related tools and resources, including datasets. A couple of these may be of use to you:
One in particular, the GGIS (Global Groundwater Information System):
USGS Surfacewater Portal also has a number of tools and resources that you may find beneficial:
NASA's GRACE Groundwater combines two major databases, again should also be very relevant here: