H25C FLC ADVISED AFTER FLT COMPLETION INTO DEN THAT THEY WERE INVOLVED IN A LOSS OF SEPARATION WITH A B737.

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I WAS ASSIGNED TO FLY A PVTLY OWNED HAWKER 1000 AS THE CAPT. MY FO AND I WERE SCHEDULED TO FLY A PAX MISSION FROM CMH TO DEN. THE FLT TO DEN WAS UNEVENTFUL; AS FAR AS WE WERE AWARE. HOWEVER; WHEN I ARRIVED AT THE HOTEL I WAS CONTACTED BY COMPANY MGMNT; WHO INFORMED ME THAT A 'LOSS OF SEPARATION RPT' IMPLICATING OUR ACFT AND A B737 ACR FLT HAD BEEN FILED BY DEN APCH CTL. THE INCIDENT APPARENTLY OCCURRED DURING THE ARR PHASE OF THE FLT. OUR FLT PLAN WAS INTO DEN VIA THE DANDD 3 ARR; OATHE TRANSITION. DURING THE FLT; WE WERE CLRED DIRECT TO BRICKYARD VOR; AND LATER DIRECT TO KANSAS CITY VOR AT FL350. SHORTLY BEFORE TURNING AT SELLS INTXN ON THE DANDD 3 ARR; WE WERE CLRED TO BEGIN OUR DSCNT TO FL220. DURING THE APCH PHASES OF FLT; THERE WRE SEVERAL ACFT ON THE SAME FREQ; WITH ALMOST CONTINUOUS RADIO XMISSIONS BTWN ATC AND VARIOUS ACFT. ON SEVERAL OCCASIONS; WE HEARD ATC STEP ON XMISSIONS FROM ACFT; OR ACFT STEP ON XMISSIONS FROM ATC. SEVERAL XMISSIONS HAD TO BE MADE A SECOND TIME; WHICH FURTHER JAMMED THE FREQ. THIS SIT PERSISTED ON EACH FREQ DURING THE ARR; APCH AND LNDG. IN THE DSCNT TO FL220; ESTABLISHED INBOUND TOWARD PRAGG INTXN ON THE DANDD 3 ARR; WE RECEIVED A FREQ CHANGE TO ANOTHER ARR CTLR; WHO IMMEDIATELY CLRED US DIRECT TO HUGO WITH A DSCNT TO 17000 FT MSL TO JOIN THE QUAIL 3 ARR. MY FO LOCATED THE QUAIL 3 ARR APCH PLATE BUT BEFORE HE COULD ENTER IT INTO THE FMS; THE SAME CTLR REVISED OUR CLRNC AGAIN TO QUAIL INTXN; DSND TO 14000 FT MSL; SLOW TO 280 KIAS; CONTINUE VIA THE QUAIL 3 ARR. WE NOTED THAT THIS CLRNC DIFFERED FROM THE PUBLISHED XING RESTR OF 250 KIAS AND EXPECT 17000 FT MSL. MY FO IMMEDIATELY ENTERED THE QUAIL 3 ARR IN THE FMS. HE THEN SWITCHED HIS RADIO TO COM #1 TO CALL THE FBO AND TO MAKE SURE THAT THE TRANSPORTATION ARRANGEMENTS WERE IN PLACE. I WAS MONITORING APCH CTL ON COM #2 AS I TURNED TO PROCEED DIRECT TO QUAIL INTXN. ATC INQUIRED AGAIN IMMEDIATELY AFTER I BEGAN THE TURN WHETHER WE WERE PROCEEDING DIRECT TO QUAIL AND I RESPONDED THAT WE WERE TURNING TO A HDG OF 281 DEGS; WHICH WAS THE DIRECT HDG TO QUAIL INTXN. I ASSUMED THAT ATC EITHER DID NOT HEAR MY FO'S RESPONSE TO THE CLRNC TO PROCEED DIRECT TO QUAIL; OR PERHAPS THAT OUR XMISSION HAD BEEN STEPPED ON. AT THE TIME OF MY RESPONSE; I HAD APPROX 10 DEGS REMAINING TO COMPLETE MY TURN TO THAT HDG. WE WERE CLRED DOWN TO 9000 FT. AT NO TIME DID ATC INDICATE TO US THAT THERE WAS ANY ACTUAL OR POTENTIAL CONFLICT WITH OTHER TFC. THE ONLY OTHER ACFT WHICH WAS CALLED OUT TO US WHEN WE WERE ABOUT 15 MI OUT FROM THE RWY ON THE LOC AT 9000 FT MSL WAS A B737 AT OUR 1 O'CLOCK POS; 5 OR 6 MI DISTANCE. WE RESPONDED THAT WE HAD THE TFC IN SIGHT; AND ATC CLRED US FOR THE VISUAL APCH; FOLLOWING THAT TFC TO RWY 35L. I FELT THAT THE ATC CTLR WAS SLOPPY IN HANDING US OFF TO THE TWR. BY THE TIME WE WERE ABOUT 4 MI ON FINAL APCH; NEITHER MY FO NOR I HAD HEARD A DIRECTION TO CONTACT TWR. THE ACFT AHEAD OF US WAS TURNING OFF THE RWY BY THIS TIME; SO MY FO CALLED TO CONFIRM OUR CLRNC TO LAND. ATC DIRECTED US TO CONTACT THE TWR; AND WE RECEIVED OUR CLRNC TO LAND FROM THE TWR WHEN WE WERE PERHAPS 2 MI OUT ON FINAL APCH. AS THE FO AND I DISCUSSED LATER; WE REALIZED THAT ATC MIGHT HAVE DIRECTED US TO THE TWR EARLIER; AND THE XMISSION COULD HAVE BEEN STEPPED ON. IF THIS DID HAPPEN; IF ATC DID NOT RECEIVE A CONFIRMATION FROM US OF A FREQ CHANGE; THE CTLR SHOULD HAVE REPEATED HIS XMISSION. OTHER THAN THIS; I DETECTED NOTHING UNUSUAL ABOUT THE RADIO COMS BTWN ATC AND OUR ACFT. IN RETROSPECT; I BELIEVE THAT SAFETY WOULD HAVE BEEN ENHANCED IF ATC CTLED FEWER ACFT ON THE SAME FREQ DURING PEAK TFC DENSITY PERIODS. OF COURSE; THIS WOULD REQUIRE MORE CTLRS DURING THESE PERIODS. SAFETY WOULD ALSO BE ENHANCED IF CTLRS AND PLTS WOULD EXERCISE MORE CARE TO ENSURE THAT THE FREQ WAS CLR PRIOR TO INITIATING A XMISSION. FINALLY; IT BEHOOVES BOTH CTLRS AND PLTS TO REPEAT XMISSIONS WHEN THERE IS NO APPARENT RESPONSE FROM THE INTENDED RECIPIENT.