B737 FAILS TO MAKE XING RESTR DURING DSCNT IN ZLC AIRSPACE.

Narrative

FMS WAS SET UP WITH ENRTE FLT PLANNED RTE; INCLUDING THE BEARR 3 ARR INTO SALT LAKE CITY. PLANNED ALT AT BEARR WAS 16000 FT; AS PER NOTE IN FLT PLAN. PLANNED DSCNT AT 300 KTS. ATC GAVE PLT'S DISCRETION TO FL240; WHILE WE WERE AT FL290 DUE TO EXPECTED TURB. I WAS FLYING AT MACH .73 DUE TO OCCASIONAL TURB. THE FL240 WAS ENTERED INTO FMS BUT NOT ENGAGED. UPON NEXT FREQ CHANGE; THE CTLR GAVE RESTR AT BEARR OF 16000 FT; 250 KIAS. THIS WAS ENTERED INTO FMS AND ENGAGED. ACFT STARTED DSCNT DUE TO PREVIOUSLY ENTERED FL240. ALT HOLD ENGAGED TO PREVENT DSCNT BECAUSE THE RIDE WASN'T BAD YET AND IT WAS TOO EARLY TO DSND. SHORTLY THEREAFTER; THE RIDE GOT WORSE AND VNAV WAS ENGAGED AND ACFT STARTED DOWN ABOUT 50 MI PRIOR TO THE TOP OF DSCNT POINT ON THE FMS. AT ABOUT 2 MI FROM TOP OF DSCNT; I SWITCHED TO THE PROGRESS PAGE AND SAW THAT WE WERE ALMOST AT BEARR INTXN; WHILE STILL AT FL200; 280 KIAS. I AM NEW TO FMS ACFT AND UNTIL THIS OCCURRENCE EVERYTHING WORKED AS EXPECTED. I FAILED TO BACK UP FMS BY CALCULATING MY OWN TOP OF DSCNT POINT AND DID NOT NOTICE WHAT IT WAS PLANNING ITS TOP OF DSCNT ON. ALL MY INPUTS INTO THE FMS LOOKED GOOD; BUT IT IS POSSIBLE DUE TO THE TIMING OF INPUTS THAT I CONFUSED IT.