A CPR HS125-1000 FLC ALLOWED THEMSELVES TO BECOME RUSHED AND ENTERED CLASS B AIRSPACE AT ATL WITHOUT PROPER CLRNC.

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WE LANDED AT NEWNAN COWETA COUNTY ARPT (CCO) TO DROP OFF PAX. WE CONTACTED DISPATCH ON THE PHONE AND WERE TOLD TO REPOS TO JAX. WE WERE ALREADY 12 HRS 50 MINS INTO OUR DUTY DAY; SO WE HAD TO HURRY TO GET TO JAX WITHIN OUR 14 HR LIMIT. WE WERE UNABLE TO CONTACT ATL APCH ON THE GND (THE FBO WAS CLOSED; THE PAY PHONE DIDN'T WORK; THE CELL PHONE SIGNAL WAS TOO WEAK BY THE TIME WE TAXIED OUT AND ATL WOULDN'T ACKNOWLEDGE US ON THE RADIO) SO I ELECTED TO DEPART VFR AND PICK UP OUR IFR CLRNC IN THE AIR. WE KNEW ATL WAS NEARBY AND I REVIEWED THE CLASS B AIRSPACE CHART AND NOTED IF WE STAYED BELOW 8000 FT MSL UNTIL 35 DME WE WOULD STAY BELOW THE CLASS B AIRSPACE. I BRIEFED THIS TO MY FO; WHO WAS THE PF. WHILE DEPARTING CCO ON A 123 DEG HDG; I WAS BUSY TALKING ON CTAF TO OTHER ACFT IN THE AREA AND TO ATL APCH TRYING TO GET AN IFR CLRNC. MY FO STARTED A CLB OUT OF 8000 FT AT 25 DME. PASSING 12700 FT; ATL APCH ASKED WHAT OUR ALT WAS AND TOLD US TO REMAIN OUTSIDE CLASS B AIRSPACE AND BELOW 14000 FT. WE LEVELED OFF AT 13500 FT AND NOTED WE WERE 30 DME FROM ATL SO WE TURNED TO 180 DEGS TO EXIT THE AIRSPACE. WE LATER DETERMINED WE WERE ALREADY ABOVE THE CLASS B AIRSPACE AT 13500 FT. WE WERE VMC AT ALL TIMES AND ARE NOT AWARE OF ANY TFC CONFLICTS. WE RECEIVED OUR IFR CLRNC AND CONTINUED TO JAX. THE PROB OCCURRED BECAUSE OF MISCOM IN THE COCKPIT. EITHER I BRIEFED THE WRONG DME OR MY BRIEF WAS MISUNDERSTOOD BY THE PF. EITHER WAY WE INITIATED THE CLB TOO EARLY AND THE MISTAKE WAS NOT CAUGHT UNTIL ATC'S VAGUE COMMENT. CONTRIBUTING FACTORS INCLUDED FATIGUE FROM A LONG DUTY DAY AND RUSHING TO COMPLETE THE TRIP WITHIN OUR DUTY LIMIT.