A LOW TIME TFC WATCH PLT TAXIED ACROSS RWY 3 WITHOUT PERMISSION AT SAT.

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I CONTACTED GND CTL (AT SAN ANTONIO) AND REQUESTED TO TAXI TO RWY 3 USING TXWY E. GND CTL REPLIED; 'TAXI RWY 3 VIA TXWY E' (OR WORDS TO THAT EFFECT). I RESPONDED; '...TAXI TO RWY 3 ON TXWY E.' AS I LOOKED TO MY L WHILE TAXIING ON TXWY E; I OBSERVED A LARGE ACFT ROLLING OUT ON RWY 12R. I THOUGHT IT MUST BE SOMETHING; THEN I LOOKED TO MY L AND SAW A LARGE ACFT HOLDING SHORT OF RWY 3. I CONTINUED FORWARD BELIEVING I WAS CLRED TO TAXI ACROSS RWY 3 TO THE RUN-UP AREA. BY THE TIME I REACHED THE RWY; I THOUGHT (FELT) SOMETHING WAS WRONG. I THOUGHT I DIDN'T ASK GND IF I WAS CLRED TO CROSS RWY 3. THIS IS WHEN GND CTL RADIOED AND TOLD ME I WASN'T CLRED TO TAXI ACROSS RWY 3 BUT TO TAXI ACROSS RWY 3 NOW TO TXWY N; THEN L TO RWY 3. THIS IS WHEN I REALIZED I HAD JUST VIOLATED; I BELIEVE; FAR 91.129I; ALBEIT UNINTENTIONALLY. TO CORRECT MY MISTAKE FROM HAPPENING AGAIN; I HAVE REREAD FAR 91.129A-I AND AIM 4-3-18(1-8). I WILL ALSO MAKE SURE I ASK ATC TO VERIFY THEIR INSTRUCTIONS BEFORE ENTERING ANY RWY AREA. IT IS MY GOAL AND INTENTION TO COMPLY WITH ALL FARS AND ATC INSTRUCTIONS FOR SAFETY REASONS. I EXPECT TO CONTINUE TO REVIEW THE FAR/AIM TO BE SURE TO STAY IN COMPLIANCE.