bower.json

{
  "name": "testcase",
  "dependencies": {
    "backbone": "1.0.0",
    "jquery": "1.10.1",
    "bootstrap": "2.3.2"
  },
  
  "exportsOverride": {
    "backbone": {
      "js": "backbone.js"	  	
    },
    "bootstrap": {
      "js": "docs/assets/js/bootstrap.js",
      "less": "less/*.less"
    },
    "jquery": {
      "js": "jquery.js"
    }
  }
}

Gruntfile.js

module.exports = function(grunt) {

  grunt.loadNpmTasks('grunt-bower-task');
  grunt.initConfig({
    bower: {
      install: {
        options: {
          verbose: true,
          cleanup: true
        }
      }
    }
  });

};

package.json

{
  "name": "testcase",
  "version": "0.0.1",
  "dependencies": {
    "grunt-bower-task": "0.2.3",
    "grunt": "~0.4.1",
    "matchdep": "~0.1.2"
  }
}