COMMUTER ACFT BEGINS RWY ENTRY TO BACK-TAXI AS CORP JET DEPARTS. NMAC.

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SCHEDULED DEP TIME FROM BDR WAS XX20 AM. TWR NOT DUE TO OPEN UNTIL XX30. REQUESTED ATC CLRNC FROM BDR FSS ON 122.2. THEY SAID CALL BACK WHEN WE WERE READY TO DEPART. THEY GAVE US THE WX; AS ATIS WAS NOT IN OP. WITH WINDS RPTED 300 DEGS AT 5 KTS WE DECIDED TO DEPART ON RWY 24 AS THIS WAS THE SHORTEST TAXI AND DEP DIRECTION WOULD APPROX OUR FLT DIRECTION. AT XX20 WE PULLED OFF THE GATE; THE FO CONTACTED FSS AND REQUESTED OUR CLRNC. FSS SAID; STAND BY; WE MIGHT HAVE TO WAIT FOR TWR TO OPEN FOR OUR RELEASE. WE PROCEEDED TO TAXI TO RWY 24. WE TAXIED ON TXWY A TO HOLD SHORT OF RWY 11/29. AT THIS POINT WE DID OUR TAXI AND PRE TKOF CHKS AND ADVISED FSS WHERE WE WERE AND WERE STANDING BY. AT ABOUT XX25 FSS GAVE US OUR CLRNC WITH A VOID IF NOT OFF TIME OF XX30. AS THE FO READ BACK THE CLRNC; I VISUALLY CHKED RWY 11/29 FOR TFC; IT WAS CLR. TO GET TO RWY 24 FROM THIS POINT REQUIRED A SHORT TAXI ON RWY 11/29; FOLLOWED BY A SHORT BACK-TAXI ON RWY 24. AS I PULLED ONTO RWY 11 AND STOPPED TO CHK RWY 24; A CORP JET HAD JUST LIFTED OFF FROM RWY 6; PASSING OVER AND IN FRONT OF US UNCOMFORTABLY CLOSE. SEVERAL FACTORS LED US INTO THIS SIT: TWR CLOSED; SHORT WINDOW OF TIME FROM DEP TIME TO TWR OPENING; ALL RWYS AT BDR REQUIRE BACK- TAXI IF FULL LENGTH OF RWY TO BE USED; NECESSITY OF USING 2 RADIOS FOR THIS OP; SHORT CLRNC VOID TIME NECESSITATED RUSHING. ATIS SAID USE 120.9 (THE TWR FREQ) TO ANNOUNCE POS AND INTENTIONS WHILE TWR CLOSED. I HAD FSS 122.2 ON TO LISTEN TO FSS. FO HAD 122.2 AND 120.9 BOTH ON. MY FO TOLD ME THAT SOMEONE HAD CALLED ANNOUNCING HIS INTENTIONS FOR RWY 6. I OBSERVED A TAXIING CESSNA AND ASSUMED THIS WAS THE ONE HE REFERRED TO. I FELT RUSHED. THE PREVIOUS TIME AT THIS ARPT; CIRCUMSTANCES WERE SOMEWHAT THE SAME; BUT BY THE TIME WE GOT OUR CLRNC; TWR OPENED AND HAD US TURN AROUND AND TAXI TO THE OTHER END OF THE ARPT; THEN WE LOST OUR DEP SLOT DUE TO VOID TIME EXPIRING. TO PRECLUDE THIS FROM HAPPENING AGAIN; I ALLOWED CREW COM TO BREAKDOWN. THE MOST OBVIOUS LESSON HERE: WHEN AT AN UNCTLED ARPT; ABSOLUTELY NO MOVEMENT ON A RWY WITHOUT BOTH PLTS MONITORING THE APPROPRIATE TFC FREQ WITH NO OTHER COM RADIOS ON .SUPPLEMENTAL INFO FROM ACN 276146: WE TURNED ONTO THE RWY AND ANNOUNCED THAT WE WERE GOING TO BE BACK-TAXIING INTO POS. PRIOR TO ENTRY RWY 24; WE STOPPED TO CHK THE RWY AND JUST AS WE STOPPED; A FALCON JET WENT PAST US AFTER DEPARTING RWY 6. NO MORE CALLS WERE HEARD OTHER THAN A SINGLE DEP CALL. POSSIBLE WAYS TO CORRECT PROB: MAKE SURE THAT ALL PLTS ARE LISTENING TO CTAF. IF A SCHEDULED ACFT DEP IS PLANNED; PERHAPS ATC COULD OPEN IN TIME TO ACCOMMODATE SCHEDULED SVC. IF ANY IRREGULARITY IS PERCEIVED; THE PLT WITH THE INFO MAKES EVERY EFFORT TO CLARIFY THE SIT AND MAKE SURE THAT EVERYONE IS THINKING ALONG THE SAME LINES.