This was tested using Ruby 2.0.0 and Rails 4.0.0.rc1.

Bower

Set the install directory for Bower components:

// .bowerrc
{
  "directory": "app/assets/components"
}

Follow the Bower instructions and create a bower.json file in your directory with your dependencies, e.g.

// bower.json
{
  // ...
  "dependencies": {
    "d3": "~3.1.0",
    "underscore": "~1.4.4",
  }
}

Include them in your JavaScript:

# config/application.rb

# include Bower components in compiled assets
config.assets.paths << Rails.root.join('app', 'assets', 'components')

// /Users/aidan/dev/code_cruise/app/assets/javascripts/application.js
//
// Bower packages
//= require d3/d3
//= require underscore/underscore
//
//= require jquery
//= require jquery_ujs
// ...

At this point, make sure your app runs and the JS libs installed by Bower are loading on the page.

Heroku

To have Heroku deploys (Cedar stack only) install and compile Bower components on push:

Use a custom Heroku buildpack that includes Node.js and Bower:

heroku config:set BUILDPACK_URL='git://github.com/qnyp/heroku-buildpack-ruby-bower.git#run-bower'

Add the following to Rakefile before the require:

# Rakefile

namespace :assets do
  desc "A little hack to make sprockets handle Bower files"
  # Add extensions to all Bower-installed files that don't have them.
  # See https://github.com/sstephenson/sprockets/issues/347
  task :precompile do
    Dir['app/assets/components/**/*'].each do |filename|
      if File.file?(filename) && File.extname(filename) == ''
        File.rename(filename, "#{filename}.txt")
      end
    end
  end
end

require File.expand_path('../config/application', __FILE__)
# ...

Change the following setting to allow assets to be compiled in production (I don't believe this is Bower-specific):
```
# config/environments/production.rb
config.assets.compile = true
```

Try a deploy: it should successfully compile assets.

It's just that easy!!! ::facepalm::

Additional resources:

renatocarvalho/gist:5923508

Bower

Heroku