A FALCON 50 CPR ACFT FLIES THE WRONG DIRECTION AFTER DEPARTING BWG AND HAS TO RECEIVE A COURSE CORRECTION TO AVOID OTHER TFC BY ZME; TN.

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ON DEP FROM BWG; I RECEIVED CLRNC (IFR) FROM LOU RADIO FOR FLT FROM BWG TO BNA. THE PF WAS MONITORING THE CTAF FOR BWG (123.0 MHZ) WHILE I WAS OBTAINING OUR IFR CLRNC ON #2 VHF. LOU RADIO ISSUED OUR IFR CLRNC 'CLRED TO BNA AS FILED. CLB AND MAINTAIN 6000 FT; CONTACT ZME ON 133.85 MHZ.' I HAD FILED THE FLT PLAN EARLIER IN THE DAY WITH ROUTING; BWG DIRECT TO BNA. THE PF SET UP THE FMS RTE ANTICIPATING ROUTING OVER HEHAW INTXN; AND ALTHOUGH WE HAD REVIEWED THE DEP; NEITHER PLT CAUGHT THE DISCREPANCY BTWN OUR FILED RTE AND THE FMS ROUTING. THIS RESULTED IN AN EXCURSION FROM THE CLRED RTE THAT CAUSED CONCERN FOR THE ZME CTLR. HE HAD INBOUND TFC TO HEHAW AT OUR ALT. THE CTLR CLARIFIED OUR ROUTING AND ISSUED A HDG CHANGE TO US. HORIZ SEPARATION REMAINED GREATER THAN 5 NM; ACCORDING TO OUR TCASII DISPLAY; THROUGH THE ENTIRE SCENARIO. THIS WAS A CLASSIC CASE OF CREW COM DEFICIENCY BROUGHT ON IN PART BY THE PF MONITORING A CTAF AT AN UNCTLED ARPT WHILE THE PNF USED ANOTHER FREQ TO OBTAIN THE IFR CLRNC. OUR COMPANY PROCS WERE FOLLOWED FOR OPS AT UNCTLED ARPTS IN WHICH THE PF MONITORS THE CTAF FOR LCL TFC WHILE HIS COPLT USES THE OTHER VHF TRANSCEIVER TO OBTAIN THE IFR CLRNC. IN THIS INSTANCE; SAFETY WAS COMPROMISED WITH THE INITIAL ERROR BEING IN THE PROGRAMMING OF THE FMS FLT PLAN WITH A ROUTING OTHER THAN THAT FILED BEFORE THE CLRNC WAS RECEIVED. SUPPLEMENTAL INFO FROM ACN 457730: OUR FMS WAS SET UP FOR THE HEHAW 3 ARR FROM BWG TO HEHAW TO BNA. WHEN WE DEPARTED RWY 21 AT BWG; WE TURNED R TO A HDG OF 245 DEGS TO PROCEED DIRECT TO HEHAW INTXN INSTEAD OF FLYING DIRECT TO BNA. TFC WAS GIVEN AT OUR ALT (10000 FT) AND 7 OR 8 MI AT OUR 11 O'CLOCK POS. WHEN WE ADVISED THE TFC IN SIGHT WE WERE GIVEN A CLRNC TO MAINTAIN A VISUAL SEPARATION AND FLY DIRECT TO BNA. THE TFC DID NOT COME WITHIN 5 MI OF OUR ACFT.