B737-300 ACFT TAXIING 'BRIDGE RTE' DIDN'T FOLLOW WRITTEN INSTRUCTIONS ON ARPT DIAGRAM CHART. FLC HAD DIFFICULTY CONTACTING GND CTL; EITHER BECAUSE OF FREQ SATURATION OR HVY CTLR WORKLOAD.

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LANDED VISUAL LAX RWY 24R; EXITED RWY ON AA CROSS RWY 24L WITH CLRNC AND TOLD TO TAXI BRIDGE RTE. (LATE AND 14 HRS 30 MINS PLUS DUTY DAY.) FO WAS IN A HURRY TO CALL LAX OPS SO WENT OFF GND TO GET GATE ASSIGNMENT. FO BACK ON BY CHECKPOINT 3 ON AA BUT GND CTL WAS STILL BUSY -- COULD NOT BREAK INTO AND CHK IN AT CHECKPOINT 3. NO OTHER TFC ON OUR WHOLE (W) SIDE OF ARPT; SO I CONTINUED TO TAXI SLOWLY ON AA TOWARD INTXN OF TXWY C. (SEE SMALL NOTE ON 10-9 LAX -- TOP R 'BRIDGE RTE'/W RTE; '...AA; HOLD SHORT OF TXWY C WHEN NUMBER ONE APCHING TXWY C...') KEEP IN MIND WHEN WE ACCOMMODATED LAX APCH BY ACCEPTING VISUAL RWY 24R; SUN IN EYES AND HAZY; HAD SUNGLASSES ON. BY THE TIME WE LANDED AND TURNED OFF -- ALMOST DARK; IE; SUN BELOW HORIZ; SUNGLASSES STILL ON. TRY TO LOOK AT 10-9 LAX SMALL NOTE WRITING TOP R WITH YOUR SERENGETI'S ON IN DARK WITH ACFT MOVING; 'ALMOST IMPOSSIBLE TO CATCH...THE HOLD SHORT OF C.' FO WAS TRYING TO BREAK ON GND 121.75 AS WE WERE APCHING TXWY C ON AA AND WE WERE THE ONLY ONE OUT THERE. LAX GND WAS GIVING VERBAL ATC CLRNC ON GND CTL. HE WOULDN'T ANSWER OUR 4 ATTEMPTS TO CHK IN. OUR B747-400 CAPT JUMP SEATER SAID 'JUST TAXI UP TXWY B AND HOLD SHORT TXWY T.' I SLOWLY DID JUST THAT INSTEAD OF HOLD SHORT OF TXWY C. I FINALLY STOPPED ABEAM OF B16 ON TXWY B AND AFTER 3 MORE ATTEMPTS TO CONTACT GND HE FINALLY ANSWERS AND VERBALLY SLAPPED OUR HAND ABOUT NOT HOLDING SHORT OF TXWY C ON AA. I STAND CORRECTED BUT WHY WAS HE SO SATURATED ON GND CTL. WHAT HAPPENED TO THE CLRNC DELIVERY GUY? IE; ON BREAK?