TAXIING TFC EXPERIENCES A RWY INCURSION.

Narrative

AFTER LNDG RWY 2L AT BNA; A R TURNOFF WAS MADE AND WE SWITCHED TO GND CTL. AFTER THE TURN ON WHAT I NOW REALIZE WAS TXWY L; WE CONTACTED GND. I WAS NOT FAMILIAR WITH THE FIELD AND TOLD GND CTL OUR DEST ON THE FIELD WAS FBO. THE TAXI CLRNC I THOUGHT I HEARD WAS TURN R AND TAXI S TO L4. WE WERE HOLDING SHORT OF A XING TXWY I BELIEVED TO BE L (DUE TO THE INSTRUCTION GIVEN) WHICH WAS ACTUALLY B. THE FO READ BACK THE CLRNC THAT I THOUGHT WAS THE SAME THAT I HAD HEARD; SO I MADE THE R TURN AND TAXIED S; ASKING THE FO TO CONFIRM THAT WE WERE ACTUALLY ON TXWY L. HE WAS HAVING TROUBLE; LOOKING AT THE ARPT DIAGRAM; WHY WE HAD MADE A R TURN. BY THIS TIME WE WERE TOLD TO STOP AND THAT WE HAD JUST CROSSED RWY 13/31 WITHOUT PERMISSION. I REALIZED THAT WE HAD CROSSED A RWY DURING OUR TAXI BUT THOUGHT IT TO BE NON-DUTY BECAUSE OPS WERE ON RWY 2L AND 2C AND I FOLLOWED AN ACFT ACROSS. CONTRIBUTING TO THIS INCURSION WAS THE FACT THAT THE TXWY SIGNS ARE CONFUSING AND THE FACT THAT THE GND CTLR DID NOT CONTEST THE TURN R TAXI S (READBACK).