It takes about 10 mins to run the checks from starting the APU to taxi, covering engine start (approx. 1 min each), anti-icing (with engines run at 100% to provide sufficient bleed air for the check), stall protection & autopilot checks. Not unduly long but I guess a bit longer than a jet which starts its engines as its pushed back & is probably ready to taxy a wee bit sooner.
The civvy operated ones I see around in the Horn of Africa on UN contracts manage to get airborne pretty quickly. Maybe it helps that they have to pay for the fuel!