BE99 ATX ON A VFR FLT PLAN HAD BEEN CLRED ENRTE. WAS MONITORING DEP CTL. SAW B737 10 O'CLOCK HEAD ON. NOSED OVER AND THE JET PASSED 200 FT ABOVE AND SLIGHTLY AHEAD. B737 APPEARED TO BE TAKING EVASIVE ACTION.

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I DEPARTED RWY 25R AT LAS WITH A VFR CLASS B CLRNC TO TURN L HDG 175 DEGS; MAINTAIN 3500 FT; EXPECT HIGHER ALT 2 MINS AFTER DEP; DEP FREQ 118.4; SQUAWK ABCD. THE DEP CTLR KEPT ME ON 175 DEG HDG THE WHOLE TIME WITH PROGRESSIVE ALT STEP-UPS TO 7000 FT. APPROX 22 MI S OF LAS; THE CTLR TERMINATED RADAR SVC; SQUAWK AB00; FREQ CHANGE APPROVED (ALTHOUGH I HAD REQUESTED ADVISORIES TO MY DEST; ONT). I REMAINED ON THE CTLR'S FREQ OF 118.4 AND SQUAWKED AB00 AND TURNED TO A HDG OF APPROX 220 DEGS MAGNETIC AND BEGAN A CLB TO 10500 FT MSL. BTWN 10200 FT AND 10300 FT MSL I SAW A B737 AT ABOUT MY 10 O'CLOCK POS HEADED RIGHT AT ME AND IT APPEARED TO BE LEVELING OFF FROM A DSCNT APPROX 200 FT ABOVE ME. I NOSED MY ACFT OVER AS I SAW THE ACFT. FROM THE TIME I FIRST SAW THE B737 UNTIL IT PASSED OVER AND SLIGHTLY IN FRONT OF ME; ONLY ABOUT 2 SECONDS OR LESS ELAPSED. I NEVER HEARD THE CTLR POINT ME OUT TO THE B737 AS TFC; NOR DID I HEAR THE PLT OF THE B737 SAY ANYTHING; BUT I'M SURE HE SAW ME; BECAUSE HE APPEARED TO BE TAKING EVASIVE ACTION AS WELL. I ESTIMATE THE ACFT CROSSED 200 FT ABOVE ME AND 100 FT IN FRONT OF ME FROM L TO R. THE CTLR SHOULD HAVE KEPT ME ON ADVISORIES UNTIL CLR OF HIS INBOUND TFC AND SHOULD ALSO HAVE ADVISED THE B737 OF MY PRESENCE. WHEN I ARRIVED ONT; I ASKED ANOTHER COMPANY PLT; WHO DEPARTED LAS APPROX 5-8 MINS BEHIND ME; IF HE HEARD ANYTHING ON THE FREQ 118.4 AND HE SAID HE HAD HEARD SOMEONE SAY; 'THAT WAS CLOSE!'