A C182 PVT PLT INADVERTENTLY ENTERS THE CLASS B AIRSPACE OF SLC WHILE ATTEMPTING COM WITH ATC AT SLC; UT.

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I TOOK OFF FROM BTF BOUND FOR SLC. THIS WAS THE FIRST TIME I HAVE FLOWN THIS RTE; ALWAYS WENT BTF TO OGD. AFTER GETTING AIRBORNE; I CALLED SLC APCH 121.10. THEY PUT ME ON HOLD. I CIRCLED OVER CITY OF BOUNTIFUL FOR 5 MINS AND DECIDED TO CALL APCH 120.90. THEY IMMEDIATELY HAD ME CALL SLC TWR 118.30. AT THIS TIME I WAS TURNING S OVER I-15 IN MY HOLD. TWR ACKNOWLEDGED; BUT DID NOT CLR ME INTO CLASS B AIRSPACE. I CONTINUED S OVER I-15 IN BTF CORRIDOR AT 5500 FT MSL. TWR ASKED MY INTENTIONS. I REPLIED 'FULL STOP AT SLC.' AT THIS TIME I FELT I WAS CLOSE TO THE CLASS B AIRSPACE; BUT I CONTINUED; ANTICIPATING CLRNC. AT THIS TIME THE SLC TWR CTLR INFORMED ME TO REMAIN CLR OF CLASS B AIRSPACE. I REPLIED I WOULD CIRCLE THE CITY. THE CTLR THEN INFORMED ME I HAD ALREADY ENTERED CLASS B AIRSPACE. I THOUGHT I WAS WITHIN THE BTF CORRIDOR AREA OUTSIDE OF CLASS B; BUT AFTERWARDS A CLOSER STUDY OF THE MAP REVEALED I DID VIOLATE CLASS B AIRSPACE. ANOTHER FACTOR THAT AFFECTED MY DECISION MAKING PROCESS WAS RAIN SHOWERS PASSING THROUGH THE BTF AND SLC AREA. TRYING TO AVOID THE RAIN/CELLS AND TIME MY ARR TO SLC BEFORE AN APCHING CELL AT SLC HAD ME ANTICIPATING TFC MERGING AND POS OF MY ACFT.