INSTRUCTOR PLT OF R44 ON INSTRUCTIONAL FLT INADVERTENTLY PENETRATED CLASS B AIRSPACE WHILE AVOIDING TFC.

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WHILE ON AN IFR TRAINING FLT OUT OF SEE A STUDENT AND I VIOLATED THE 3800 FT SHELF OF MIRAMAR'S B AIRSPACE. WHILE ENRTE TO THE JLI VORTAC; DIRECT FROM SEE; I ADVISED MY STUDENT TO CLB TO 7000 FT; BUT TO CLB AT ABOUT 500 FPM AT 80 KIAS AND THAT I WOULD ADVISE OF A LEVELOFF. I LOOKED DOWN AT THE TCAS AND IT INDICATED THAT THERE WAS AN ACFT SLIGHTLY ABOVE US TO THE SE. I LOOKED OVER AND SAW A C172; POSSIBLY A C152. WE WERE MONITORING SOCAL ON 132.2; WITH THE INTENT TO CONTACT THEM FOR A PRACTICE APCH INTO RMN. I NOTICED THE CESSNA MAKE A SLIGHT TURN TOWARD US; SO I ADVISED THE STUDENT TO CLB AT A FASTER RATE AND THE CESSNA WOULD PASS UNDER US ABOUT 300 FT WITHOUT INCIDENT. I KEPT MY EYES ON THE CESSNA AND IT APPEARED TO BE MAKING A TURN BACK EBOUND. I MAINTAINED A VISUAL UNTIL I WAS SURE THE TFC WAS GONE. AS I LOOKED BACK INTO THE COCKPIT; WE WERE NOW AT 4400 FT MSL AND HAD JUST TRANSITIONED THROUGH THE FAR S SIDE OF THE 3800 FT SHELF OF MIRAMAR'S B AIRSPACE. IF I WOULD HAVE CONTACTED SOCAL EARLIER; I COULD HAVE RECEIVED B AIRSPACE CLRNC AND POSSIBLE FLT FOLLOWING FOR TA'S. I SHOULD HAVE COMMUNICATED WITH MY STUDENT BETTER TO LET HIM KNOW WHICH ALTS TO ADHERE TO. I ALSO COULD HAVE BEEN MORE SITUATIONALLY AWARE. I'M NOT EVEN 100% SURE WE BLEW THROUGH THE B AIRSPACE SHELF BUT THERE WAS NO INTENT BEHIND MY MISTAKE.