Based on rekkas work I extended the docker image by adding the optional ability to run biber. It uses latest tectonic at the time of writing (0.1.10). Its a little bit bigger ~75mb (for obvious reasons 
) .
You can find the image here:
https://hub.docker.com/r/dxjoke/tectonic-docker/
The code you can find here:
EDIT: Updated image to 0.1.11