I have added bootstrap to my site. Here is the structure I am using. (I cannot whatsoever remove the bootstrap.css file since it I modified it to my liking).
I was also struggling to make boostrap3 glyphicon work in rails 4. I solved it by adding
@font-face {
font-family: 'Glyphicons Halflings';
src: url(asset_path('glyphicons-halflings-regular.eot'));
src: url(asset_path('glyphicons-halflings-regular.eot?#iefix')) format('embedded-opentype'), url(asset_path('glyphicons-halflings-regular.woff')) format('woff'), url(asset_path('glyphicons-halflings-regular.ttf')) format('truetype'), url(asset_path('glyphicons-halflings-regular.svg#glyphicons_halflingsregular')) format('svg');
}`
to application.css.scss file and
config.assets.paths << "#{Rails}/vendor/assets/fonts"
to application.rb file.