The Central Valley Green Way parallels the Sky Train route for a good part of it's distance between the East side of Vancouver and into adjoining Burnaby and New West, you can also take the older 7 11 off road pathway through another part of New Westminster and along a more southerly Sky Train route and then onto quieter side streets, there are a good number of bicycle orientated routes trans versing Vancouver North to South and East to West, plus you can take your bike onto the Sky Train on off peak hours and all buses have bike racks mounted up front, limit is only two bikes though.
I have traveled all over the Lower Mainland ( comprising Vancouver, North and West Vancouver, Richmond,Burnaby, New Westminster, Surrey, Coquitlam, Port Coquitlam, Port Moody, Pitt Meadows and Maple Ridge, quite a fair sized area and with the bike lane open on the new Port Mann freeway bridge into Surrey as well as a widening of the pathway over the Second Narrows into North Vancouver there is easier and safer access even if one is close to a lot of traffic depending on where you go.
The Evergreen extension of the Sky Train elevated system from Burnaby into Coquitlam makes it even easier to get out further with your bike, although I tend to ride everywhere it is nice to have the option if you are tired or do not have the time.