CPR CREW TAXIED WRONG DIRECTION AT UNFAMILIAR ARPT WHILE FO PROGRAMMED FMC. CROSSED ACTIVE RWY WITH NO TFC. REDIRECTED BY GND CTLR.

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WE HAD JUST FINISHED OUR AFTER START CHKLIST AND WE WERE CLRED TO TAXI TO RWY 24 VIA TXWY E AND TXWY C FROM THE FBO AT BDL BY GND CTL. I READ BACK THIS CLRNC AND THE CAPT BEGAN TO TAXI AS I WENT TO WORK ENTERING OUR ROUTING INTO THE FMS. THE CAPT ASKED ME WHERE TXWY E WAS AND I LOOKED UP AND POINTED TO THE TXWY OUT THE WINDOW THAT WAS LABELED ECHO FROM ITS SIGN 'E.' I THEN WENT BACK TO THE FMS. WITHOUT ME REALIZING IT; THE CAPT FOUND TXWY E; BUT TAXIED THE WRONG WAY ON TXWY E AND CONTINUED THE WRONG WAY ON TXWY E XING AN ACTIVE (BUT NOT IN USE AT THE TIME) RWY; RWY 33. RWY 24 WAS THE PRIMARY RWY (AT LEAST THE PRIMARY RWY FOR JETS). AS WE WERE XING RWY 33; I REALIZED; AND THE CAPT REALIZED; SOMETHING WASN'T RIGHT; AND THEN GND CTL CALLED US ASKING US IF WE WERE GOING TO RWY 24. IN OTHER WORDS; HE WAS WONDERING WHAT WE WERE DOING. I SAID YES WE WERE GOING TO RWY 24 AND THAT WE WERE APPARENTLY LOST. HE CASUALLY TOLD US TO TURN AROUND RECROSS RWY 33; BACK-TAXI ON RWY 1; JOIN TXWY C AND TAXI TO RWY 24. THAT WAS THE END OF THE EVENT. WE WERE LUCKY TO HAVE A PATIENT GND CTLR BECAUSE THIS WAS A BIG SCREW-UP ON OUR PART. ALSO; WE WERE LUCKY THAT RWY 33 WAS NOT IN USE AT THE TIME. I MISTAKENLY LET MYSELF GET DISTR WITH THE FMS WHILE AT THE SAME TIME I MISTAKENLY ASSUMED THE CAPT WAS FAMILIAR WITH THE TAXI RTE (AFTER ACKNOWLEDGING HE KNEW WHERE TXWY E WAS). THE PROB WAS NEITHER ONE OF US BOTHERED TO LOOK AT THE ARPT LAYOUT WHICH LED TO US TAXIING THE WRONG WAY ON TXWY E.