Correcting Worldview-3 data to ground reflection/bottom of atmosphere with open source?

Converting WV3 data to ToA reflectance is fairly straight forward and is well documented in the official documentation.

Basically, the approach is to go from DN to ToA radiance (L), using this formula:

L = GAIN * DN * (abscalfactor / effectivebandwidth) + offset

These parameters can be found in the metadata of your satellite image.

From ToA radiance to ToA reflectance, the calculation is:

R = (L * d_es^2 * pi) / (E_sun * cos(theta))

With: d_es being the earth-sun distance at the time of acquisition (in AUs).
E_sun is the band-averaged solar irradiance at 1 AU.
theta being the solar zenith angle.

More details can be read in the documentation. All of the above is already available as a unofficial python package made available by my colleagues at https://github.com/DHI-GRAS/dg-calibration (note that this is code that is used internally only, and no support is available).

With the above, the main challenge is going from ToA to BoA information. For that, you can use Py6s - https://py6s.readthedocs.io/en/latest/. It is not the easiest bit of code to set up, but it is Python.