BE30 PLT FLEW ACROSS THE RWY 28R APCH PATH WHEN HE WAS CLRED TO LAND ON RWY 28L AT SFO. HE CONFLICTED WITH AN ACR B737.

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ON DEC/SUN/01; AT APPROX XA30 I WAS TOLD BY BAY APCH TO FLY 250 DEG HDG TO JOIN THE SFO 095 DEG RADIAL AND WAS CLRED FOR THE QUIET BRIDGE VISUAL APCH. I WAS INSTRUCTED TO MAINTAIN AT LEAST 230 KTS. I WAS TOLD TO FOLLOW B747 TFC AHEAD. THAT TFC WAS IN SIGHT. THERE WAS ALSO 10 O'CLOCK TFC; A B737 WHICH I ALSO HAD IN SIGHT. I SET MY #1 NAV TO SFO 095 DEG RADIAL AND WHEN IT CAME IN SLEWED MY HEADING BUG TO 095 DEGS. I THEN SET THE #2 NAV TO SFO 095 DEG RADIAL AND THE #1 NAV TO THE RWY 28R LOC. ASSUMING THAT THE SELECTED HEADING WOULD TAKE ME ALONG THE SFO 095 DEG RADIAL TO THE HIGH SPAN OF THE SAN MATEO BRIDGE WHERE I WOULD JOIN THE LOC; I DIVERTED MY ATTN TO COMPLETING THE DSCNT AND APCH CHKLISTS. APPARENTLY; THE AUTO SLAVING FEATURE ON THE #1 DIRECTIONAL GYROSCOPE WAS NOT WORKING PROPERLY BECAUSE THE DIRECTIONAL GYROSCOPE WAS POINTING THE ACFT 20 DEGS L OF THE DESIRED HEADING. BTWN TRACKING THE OTHER ACFT AND COMPLETING THE CHKLISTS MY ATTN WAS DIVERTED LONG ENOUGH TO CAUSE ME TO FLY ACROSS THE RWY 28R LOC AND INTO THE RWY 28L LOC COURSE. I THEN NOTICED THAT I WAS APCHING THE S SHORE OF THE BAY AND WAS NOT HEADING TOWARD THE HIGH SPAN OF THE BRIDGE AND HAD GONE FULL SCALE ON THE RWY 28R LOC. IT WAS THEN THAT I NOTICED THE HEADING PROB. I TURNED THE ACFT TO THE R TO GET MYSELF BACK ON COURSE AND SELECTED THE FREE SLAVING MODE AND REALIGNED THE #1 DIRECTIONAL GYROSCOPE. AT ABOUT THIS TIME THE B737; WHO WAS TALKING ON A DIFFERENT APCH FREQ CROSSED BEHIND ME AND ESTABLISHED ITSELF ON THE RWY 28R FINAL. I WAS THEN INSTRUCTED TO CONTACT THE TWR. WHEN I DID; THE CTLR CLRED ME TO LAND ON RWY 28L. I HAD A FEELING THAT I HAD CAUSED SOME TROUBLE; BUT WAS NEVER TOLD THAT I WAS S OF COURSE BY THE APCH CTLR. WHEN I LANDED AND CONTACTED GND I WAS TOLD THAT I HAD A MESSAGE FROM BAY APCH TO GIVE THEM A CALL. WHEN I DID THEY TOLD ME THAT THERE WOULD BE A DEV RPT FILED.