Here was the config option I needed in config/application.rb:
config.action_controller.relative_url_root = '/sub'
I would guess it's because the Apache/Passenger directive doesn't take effect when precompiling assets (e.g. the Bootstrap SASS) so you need to let the precompiler know where the fonts will be. Thanks for the help, wkaha and archie, and here's the ilnk on the bootstrap-sass github that clued me in: https://github.com/thomas-mcdonald/bootstrap-sass/issues/443