{
  "name": "bootstrap-social",
  "main": "bootstrap-social.css",
  "license": "MIT",
  "ignore": [
    "assets",
    "index.html",
    "LICENCE"
  ],
  "dependencies": {
    "bootstrap": "~3",
    "font-awesome": "~4.3"
  }
}

{
  "name": "bootstrap-social",
  "main": "bootstrap-social.css",
  "license": "MIT",
  "ignore": [
    "assets",
    "index.html",
    "LICENCE"
  ],
  "dependencies": {
    "bootstrap": "~3",
    "font-awesome": "~4.4"
  }
}

Update Bower to require Font-Awesome 4.4
Update Bower to require Font-Awesome 4.4

Looks like you got all the base files for 4.4 included but forgot to update your bower file dependencies.