BEC90 CREW ALMOST COLLIDED WITH A GLF4 TAKING OFF IN THE OPPOSITE DIRECTION AT DTS.

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G4 DEPARTED RAMP AS WE ENTERED ACFT. WE PERFORMED NORMAL START ROUTINE AND BEGAN TAXI TO RWY 14 AND ANNOUNCED INTENTIONS ON CTAF. WE FOLLOWED ANOTHER ACFT TO DEP END OF RWY 14 WHILE CALLING EGLIN CLRNC DELIVERY AND RECEIVING CLRNC. AFTER A DELAY OF MORE THAN 5 MINS WHILE HOLDING FOR 2 ARRS TO RWY 14 AND FOR DEP OF THE ACFT TAXIING AHEAD OF US WE RECEIVED DEP RELEASE FROM EGLIN DEP CTLR. WE ANNOUNCED ON CTAF THAT WE WERE ENTERING RWY 14 FOR DEP AND BEGAN TKOF ROLL. SUBSEQUENTLY THE G4 ANNOUNCED THAT HE HAD ENTERED RWY 32 AND HAD CROSSED THE HOLD LINE. I COULD SEE HIS ANTI-COLLISION LIGHTS AND DETERMINED THAT HE WAS NEAR TO; BUT NOT ON THE RWY SURFACE. HE APPEARED TO BE HOLDING POS. SINCE WE WERE NEAR TO ROTATION SPD WE CONTINUED TKOF AND CROSSED WELL ABOVE THE POTENTIAL CONFLICT. THE G4 SUBSEQUENTLY DEPARTED RWY 32 VFR AND CALLED EGLIN DEP REQUESTING IFR CLRNC. HE TOLD THE CTLR THAT HE HAD BEEN UNABLE TO ESTABLISH RADIO CONTACT WITH ATC PRIOR TO DEP. WHILE WE FOLLOWED PROPER PROCS AND MONITORED CTAF CONTINUOUSLY DURING TAXI; WE MAY HAVE MISSED THE G4 ANNOUNCEMENT DUE TO FREQ CONGESTION. I SHOULD HAVE BEEN BETTER AWARE OF OTHER SURFACE MOVEMENTS; BUT BOTH MY COPLT AND I LOST AWARENESS THAT THE G4 WENT SOMEWHERE. THE G4 CREW IGNORED LCL PROCS; DEPARTED OPPOSITE PREVAILING TFC WITHOUT ATC RELEASE IN A DIRECTION THAT WOULD TAKE THEM QUICKLY INTO EGLIN AFB TFC AREA.