BE20 AND B737 HAD LESS THAN COMFORTABLE SEPARATION IN L30 CLASS E.

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AFTER DEPARTING LSV ON A FILED VFR FLT PLAN WITH A PUBLISHED CLASS B DEP RTE; I WAS INSTRUCTED BY NELLIS TWR TO CONTACT NELLIS DEP. THE CTLR ASKED WHAT OUR INTENTIONS WERE. I TOLD HIM THAT WE WANTED TO CLB TO 14500 FT MSL AND FLY A HEADING OF 215 DEGS. THE NELLIS CTLR SAID THAT HE WOULD GIVE 'LAS VEGAS A CALL.' AFTER APPROX 10 SECONDS; THE NELLIS CTLR CLRED US TO CLB THROUGH THE CLASS B AIRSPACE ON COURSE. I BEGAN A CLB AND A TURN ON COURSE. AFTER PASSING THROUGH 9600 FT MSL; THE NELLIS CTLR STATED 'RADAR SVC TERMINATED; SQUAWK 1200 AND CONTACT LAS VEGAS APCH ON 125.02.' WE CALLED UP LAS VEGAS APCH; GAVE A POS RPT 'OUT OF (APPROX) 9800 FT FOR 14500 FT' AND THE CTLR ASSIGNED A SQUAWK CODE. AFTER APPROX 60-90 SECONDS; THE CTLR SAID; 'BE20 TURN RIGHT NOW TFC ALERT HEADING 260 DEGS.' AS WE TURNED HEADING 260 DEGS; WE SAW AN ACFT AT OUR 12 O'CLOCK POS HIGHER THAN OUR ALT. I ARRESTED THE CLB AND BEGAN A DSCNT OUT OF 12800 FT MSL BECAUSE IF WE CONTINUED THE CLB TO 14500 FT THERE WOULD BE A POSSIBLE TFC CONFLICT. THE CTLR WAS INSTRUCTING US TO 'MAINTAIN 1200 FT;' HOWEVER I WAS PAST THAT ALT; AND HAD ALREADY INITIATED A DSCNT BACK DOWN TO 12500 FT. THE TFC WAS ACR ACFT AND I HEARD HIS RADIO CALL TO THE CTLR THAT HE HAD TO FOLLOW AN RA FROM THE TCASII. THE PLT OF THE ACR Y ALSO ASKED THE CTLR IF SHE WAS TALKING TO US. APPROX 3 MINS AFTER THE SIT; THE CTLR TOLD US 'RADAR CONTACT.' I FEEL THAT SOME OF THE CONTRIBUTING FACTORS WAS FAILURE OF THE PLTS FOR BOTH ACFT TO SEE AND AVOID EACH OTHER. ALSO; IT WAS A SEVERE CLR DAY AND I THINK THAT ACR Y MAY HAVE BECOME COMPLACENT IN THEIR RESPONSIBILITY IN SCANNING FOR TFC. THE BOTTOM LINE IS THAT WE JUST DIDN'T SEE THEM AND IT WAS A GOOD THING THAT WE WERE TALKING TO LAS VEGAS APCH ESPECIALLY SINCE IT'S NOT REQUIRED FOR VFR FLT. WHEN I LANDED; I CALLED LAS VEGAS APCH ON THE TELEPHONE AND SPOKE TO A SUPVR TO APOLOGIZE FOR THE SIT. HE INFORMED ME THAT HE WAS AWARE OF THE SIT THAT OCCURRED AND EMPHASIZED ON THE IMPORTANCE OF DILIGENCE IN 'SEEING AND AVOIDING' AND THAT THE AIRSPACE AROUND LAS VEGAS IS GETTING BUSIER EVERYDAY; HOWEVER WE STILL HAD VFR SEPARATION REQUIRED BY REG. ALL PLTS WHETHER ON A VFR OR IFR FLT PLAN OR WHETHER THEY ARE FLYING A C152 OR B737 NEED TO SEE AND AVOID.