Update (Jan 2019): Bower hasn't been maintained for years, and using Bower packages should now be considered a discouraged practice.
This seems pretty easy until you realize that Bower (a Node.js package) is not available in the Heroku Ruby build pack. The gem bower-rails allows for easy Bower integration into Rails, but it won't work out of the box in Heroku.
Use the Multi buildpack to combine Ruby and Node buildpacks.
I recommend locking the versions (
#v60) to ensure that you get versions that interoperate together (in case one upgrades and breaks interoperability).
The last pack defined (Ruby in this case) is the "main" one that defines the process types (web, console, etc).