I’ve appreciated being able to use the byCycle trip planner in Portland, Oregon to plan my bike trips through the city on the easiest, safest and most enjoyable routes.
If your area already has an online transit trip planner (fairly common) but not a bicycle trip planner (uncommon), and would like to introduce a bicycle trip planner, the byCycle blog has a post on what it takes to add a new area to byCycle.org: money and data. You can can use the open source code to install and maintain your own byCycle trip planner. Full details are in this blog post.
After all, bikes and transit belong together.
Below, a screenshot of the trip planner.