PA28 INSTRUCTOR AND STUDENT ENTERED SCT CLASS B WITHOUT CLRNC.

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INTENDED RTE OF FLT; DEPARTING VFR FROM POC; 2 ACFT WITH FLT FOLLOWED WITH ATC; INTERCEPT 215 DEG RADIAL FROM POC; CLBING TO 4500 FT MSL DIRECT 'QUEEN MARY' AND THEN REQUEST SHORELINE TRANSITION TO N; SAN FRANCISCO; FINAL DEST 'RIO VISTA' (088). WE WERE IN CONTACT WITH ATC SINCE GND; THEN TWR; SOCAL 125.5 PASSED TO NEXT CTLR (CLASS B). THE INITIAL CONTACT WAS 'YOU PENETRATED THE CLASS B AIRSPACE WITHOUT CLRNC; TURN TO 020 DEGS TO THE L.' IT WAS A DELAYED REACTION ON THE PVT PLT WHICH INTERFERED AS AN INSTRUCTOR AND MADE HIM TO COMPLY WITH INSTRUCTION FROM ATC. WE WERE THEN DIVERTED BY ATC 360 DEGS TO THE L AND AWAY FROM CLASS B; WHEN WE PROCEEDED TO RIO VISTA; FIRST DIRECT TO VOR (FILMORE) CLBING TO 10500 FT MSL; NAVING VOR TO VOR; PILOTAGE AND DEADRECKONING. WHEN WE FINISHED OUR TRIP OUR CHIEF INSTRUCTOR AT ZZZ; PREVIOUSLY CONTACTED BY ATC; INSTRUCTED US OF OUR MISTAKE; WHICH WAS VIOLATING CLASS B WITHOUT CLRNC. WE SUPPOSED TO ASK FOR A CLRNC TO PASS THROUGH CLASS B AND BE CLRED BY ATC TO GO THROUGH. THE PVT PLT AND THE PLT FROM THE SECOND AIRPLANE ARE FROM SWITZERLAND AND GERMANY. IT WAS THE FIRST TIME I FLEW WITH THEM EVEN THOUGH THEY SHOWED ME AND DISCUSSED THE PREFLT; AND TRIP PLANNING WITH ME. THEY WERE WELL PLANNED. THE DIVERSION MENTIONED; TO GO TO THE 'QUEEN MARY' AND TRAVELING ALONG THE COAST; BECAUSE IT WAS A BEAUTIFUL DAY; THE INTENT WAS TO GET A CLRNC TO GO THROUGHOUT CLASS B. THAT IS WHY WE DECIDED TO GET FLT FOLLOWING AND TRY TO GET A CLRNC. THE INITIAL PLANNING WAS 'POE;' FILMORE VOR AND THEN THE FOLLOWING VORS THROUGHOUT THE SAN JOAQUIN VALLEY AND FINALLY '088.'