CL65 ACFT WITH TAXI CLRNC TO HOLD SHORT OF INTXN. DURING TAXI RPTR FO WAS DISTR WITH THE CHKLIST AND ASSUMING THE CAPT KNEW WHERE THE INTXN WAS; DIDN'T CATCH PASSING THE INTXN UNTIL THEY WERE XING A RWY.

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AT XA40 WE BEGAN OUR TAXI FROM THE GATE. ATIS STATED WE SHOULD EXPECT RWY 20L/R/C. OUR TAXI CLRNC WAS COPIED AND READ BACK INITIALLY BY THE CAPT. THIS READBACK WAS NOT VERIFIED BY THE CTLR; AS OTHER ACFT WERE MAKING CALLS. I FINALLY READ BACK THE CLRNC AS 'FROM T1 TO RWY 13 VIA S ON TXWY B TO TXWY B4; HOLD SHORT OF RWY 20R.' AS I READ THIS WE WERE ON T1 TURNING S ON TXWY B. THE READBACK WAS CONFIRMED BY THE CTLR. I UNDERSTOOD THE CLRNC; AND FELT THE CAPT WAS COMFORTABLE AND UNDERSTOOD THE INSTRUCTIONS ALSO. WE DELAYED THE TAXI CHKLIST UNTIL THIS POINT; SO THE CAPT NOW CALLED FOR THE TAXI CHKLIST. WE TAXIED S ON TXWY B AS I BEGAN MY TAXI CHKLIST DUTIES. MY FUNCTIONS DURING TAXI REQUIRE MY EYES TO BE INSIDE THE COCKPIT. THE CAPT TAXIES THE AIRPLANE AND IS PRIMARILY RESPONSIBLE FOR TAXI SAFETY. OF COURSE; I SHARE THIS RESPONSIBILITY AND WAS OCCASIONALLY LOOKING OUTSIDE TO VERIFY WE WERE FOLLOWING INSTRUCTIONS AND CLR OF OBSTRUCTIONS. AS I CONTINUED MY DUTIES INSIDE THE AIRPLANE I HEARD THE CAPT STATE SOMETHING TO THE EFFECT OF 'I HAVEN'T SEEN B4 YET; I'M XING RWY 13; CLR L.' THIS GOT MY ATTN QUICKLY BECAUSE IT WAS NOT IN OUR CLRNC. I IMMEDIATELY STATED; 'NO; WE'RE NOT CLRED TO CROSS RWY 13.' AS I SAID THIS; I REALIZED WE WERE ALREADY ON RWY 13; SO I SAID 'GO; GO; GO!' TO GET HIM TO QUICKLY TAXI OFF. WE CROSSED RWY 13 AND STOPPED CLR ON TXWY B S OF RWY 13. AFTER ABOUT 20 SECONDS THE GND CTLR STATED 'LOOKS LIKE YOU WENT A LITTLE TOO FAR; TURN R ON TXWY K; HOLD SHORT OF RWY 20R.' WE COMPLIED; AND THE REST OF THE FLT WAS UNEVENTFUL. PRIOR TO TKOF; THE CAPT WAS ASKED TO CALL THE BNA TWR UPON ARR IN CVG. STERILE COCKPIT MAY HAVE BEEN BREACHED OCCASIONALLY DUE TO THE IMPACT OF THE EVENT. A FO ON THE CL65 IS VERY BUSY INSIDE THE COCKPIT WHILE TAXIING FOR DEP. IT IS ALSO MY JOB TO ASSIST THE CAPT WITH ACFT MOVEMENT. HOWEVER; I CAN'T DO EVERYTHING AT ONCE. IF THE CREW IS UNSURE OF A CLRNC; THE AIRPLANE SHOULD BE STOPPED UNTIL THE CONFUSION IS CLRED UP. ON THIS NIGHT I HAD NO INDICATION THAT THERE WAS ANY MISUNDERSTANDING. SINCE IT WAS DARK OUTSIDE AND RAINING; EVERYTHING APPEARED NORMAL (AND WAS NORMAL FOR PART OF THE TAXI) WHEN I WAS LOOKING OUTSIDE. THE CAPT STARTED BOTH ENGS AT THE GATE AND BRIEFED MYSELF AND THE FLT ATTENDANT ON A SHORT TAXI IN ANTICIPATION OF A RWY 20R DEP; SO INITIALLY I FELT SOME PRESSURE TO COMPLETE MY DUTIES AT A FASTER PACE. THE RWY CHANGE ALSO REQUIRED ME TO RECOMPUTE THRUST SETTINGS AND ALLOWABLE WTS; AS WELL AS REVIEW DEP PROCS. HAD I KNOWN OF HIS CONFUSION; I WOULD HAVE STOPPED AND GUIDED HIS TAXI WITH THE ARPT DIAGRAM OR CALLED GND FOR A PROGRESSIVE TAXI. SUPPLEMENTAL INFO FROM ACN 395070: WAS GIVEN TAXI CLRNC FROM T1; S ON TXWY B; TXWY B4 HOLD SHORT OF RWY 20R TO RWY 13. WE PASSED UP B4 AND CROSSED RWY 13/31. SOME FACTORS WHICH MAY HAVE LED TO THE CONFUSION WERE: WE WERE EXPECTING RWY 20R AS STATED ON ATIS AND WERE GIVEN RWY 13. THE FIRST 2 ATTEMPTS TO READ BACK CLRNC WERE INTERRUPTED; WAS LISTENING TO PIREP DURING TAXI; AT NIGHT; WINDSHEAR; RAIN. I WAS UNFAMILIAR AND ASSUMED FO WAS LOOKING AT CHART. NEVER DID SEE B4. WAS DEPENDING ON PROGRESSIVE BY FO. FO THOUGHT I KNEW WHERE B4 WAS.