The good news: the City of Ottawa has been steadily increasing its support for cycling, including a dedicated bike lane trial downtown.
The bad news: the official cycling map site, http://www.capitalcyclingmap.ca/ is awful, with incredibly awkward pre-GoogleMaps navigation and no real interactivity.
The good news: the city has released its bike routes data on its open data site, so now anyone can make a better map, apps, and integrate the cycle map info onto websites. (There was an initial glitch with the release, but the files are now up.)
Ottawa Open Data Catalogue - Ottawa Cycling Network
formats available are KML (Google Earth format), SHP and DWG.
Here's a wide view of the KML data (the cyan grid lines and other colours layered around Ottawa in the centre - Ottawa covers a huge area):
Ottawa's Mayor, Jim Watson, is a cycling supporter and does a good job of interacting on Twitter. Here's a little Storify of how things spread through Twitter: