Are there any Part 135 (On-Demand Passenger Charter) companies out there that use Aviation Bio-Fuel?
Biofuel has already been considered and tested on some aircrafts. Here you can find an article about tests.It states at least six of them


  At least six airlines, including KLM, Lufthansa and Finnair, have now
  used biofuel on flights carrying passengers.


However there is still a long way to go.On wikipedia it says  


  The sustainable aviation fuels certification and production pace seems
  insufficient to meet the IATA target of halving the CO2 emissions by
  2050


But airports do not supply bio-fuels for now since you need tons, even for one flight.

And for the list that used biofuel on their commercial flight you can check this list out. On that list i know KLM, interjet,Hainan offers charter flight. So it is safe to say those companies environmentally conscious, if you want.