Bo Bozz Nørgaard is a visual artist, designer and photographer who was the lead artist on the Drilling Billy, and created all of the 3D models.
A 3D print from the original model file
It's not known what modelling software he used, but it can be assumed it was some early version of 3D Studio. Apparently Bo still has all of the original 3D models as in 2014 he created a 3D print of Billy.