GOV PLTS ENTER CLASS B AIRSPACE WITHOUT CLRNC AFTER DEPARTING AN UNDERLYING ARPT.

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AFTER LNDG AT MKC; WE REFUELED THE ACFT AND CONTINUED OTHER DUTIES SEPARATELY; SO AS TO EXPEDITE OUR DEP FROM MKC TO COS AND BACK TO DMA. UPON GETTING READY TO REBOARD THE ACFT; I ASKED THE OTHER PLT ON THE TRIP; IF HE HAD FILED A FLT PLAN; TO WHICH HE STATED; WE WOULD DEPART VFR. I BELIEVED WE WERE GOING TO GO IFR; HOWEVER I SUSPECTED HE KNEW SOMETHING I DIDN'T. WE STARTED AND TAXIED; GND ASKED IF WE HAD A FLT PLAN. WE ADVISED THEM WE WERE DEPARTING VFR IN VFR CONDITIONS; TO WHICH THEY ACKNOWLEDGED IN A SURPRISED TONE; TO TAXI TO RWY 1 AND CONTACT TWR WHEN READY. WE WERE CLRED FOR TKOF WITH INSTRUCTIONS TO MAKE A L TURN ON COURSE. WE DID AS INSTRUCTED. I CONTINUED TO NAV IN VFR CONDITIONS; LOOKING FOR OTHER TFC CLBING OUT; WHILE THE OTHER PLT HANDLED THE RADIOS. I HEARD HIM ASK TWR FOR A FREQ CHANGE. WHEN HE CONTACTED THIS FREQ; THEY IMMEDIATELY INSTRUCTED US TO CHANGE TO ANOTHER FREQ. WHEN WE CONTACTED THIS FREQ THE CTLR ASKED OUR POS; GAVE US A TFC CALLOUT AND A SQUAWK CHANGE. AFTER WE WERE CLR OF TFC; WE CLBED TO 16500 FT WITH FLT FOLLOWING; AT WHICH TIME THE CTLR GAVE US A PHONE NUMBER TO CALL UPON OUR ARR AT COS. WE CONTINUED OUR FLT WITH FLT FOLLOWING TO COS. UPON CALLING THE NUMBER IN KANSAS CITY; WE WERE INFORMED WE HAD ENCROACHED INTO CLASS B AIRSPACE. AT NO TIME WAS I AWARE WE HAD ENTERED INTO CTLED AIRSPACE WITHOUT CLRNC UNTIL ARRIVING IN COS. LOOKING BACK ON THIS I COULD HAVE QUERIED THE OTHER PLT FOR MORE INFO; QUERIED TWR AS TO THE SURPRISED TONE IN THEIR VOICE WHEN WE REQUESTED VFR; TWR COULD HAVE NOTIFIED US OF THE CLOSENESS OF THE AIRSPACE.