Flights & getting there
The road between Tamale and Mole National Park is now paved, greatly reducing journey times. A charter taxi from Tamale will cost around C400 return. Grassroot Tours Ghana can take you for the day in a 4WD with a driver for C350 excluding fuel – the advantage being that a park ranger will be able to accompany you in the car, so you won't need to hire a park vehicle.
If coming by public transport from Tamale, you could get a tro-tro (minibus) headed for Wa, and ask to be dropped at Damongo or Larabanga, from where you can get a taxi or motorbike to the park. From Larabanga you could even hike or bike, if there's enough daylight (one to two hours walking, depending on your level of fitness).
The Metro Mass bus from Tamale to Mole wasn't running at the time of research, but you could catch the 5am service from Tamale to Wa, changing at either Damongo or Larabanga to get to the park.