When I used to work in Vancouver, I would mix it up. SkyTrain is an issue with bikes in rush hour, so keep that in mind. WCE works better to bring the bike into town in the morning and is only 19minutes to downtown from PoMo station.
As for riding, riding up and over Bby Mtn is not time efficient, but it is lifestyle satisfying if you are on a cross bikeā¦ just to bypass the tediousness of Barnett Highway. Coming from Vancouver, I'd take some varying combination of Hastings/Adanac/Francis-Union to get to either Barnett or Bby Mtn.
For Burnaby Mtn, I prefer the climp up Pandora's, but you can also use the TCT gravel climb. Then through the Rose Garden and down any of the east side trails - TCT, Nicole's, Jump Trail, GJ - all doable to some extent on a cross bike. Then you pop out in Glenayre and burn down Clarke Hill to St. Johns.
Barnett Highway Eastbound is Waaaay better that Westbound, which is a tedious false flat and freaking cold in the morning (shady side of the mountain). But much quicker than over Bby Mtn.
If you want to get to the Production Way side to ride the BMUT to either Broadway or Francis/Union, then it's best to grind up Clarke Hill (much nicer now that they have a sidewalk on the west side), then burn down to Gaglardi and hit the BMUT. Much longer, but another option for variety.