I don't think you can do this with CDN cause you can not apply the style on the div only (try a iframe?).
What you can do is try to compile the minimum css required and apply this on your div.
Download the latest version of Bootstrap from Github.
Copy every bootstrap class you will use to a subclass of #login-form in Less like:
#login-form .row {.row;}
Add this lines to the end of bootstrap.less and compile this files, copy the latest lines of the resulting CSS the #login-form
For your example i use:
#login-form .row {.row;}
#login-form .col-md-7 {.col-md-7;
float: left;
width: percentage((7 / @grid-columns));
}
#login-form .form-group {.form-group}
#login-form .btn {.btn;}
#login-form .btn-primary {.btn-primary;}
#login-form .form-control {.form-control;}
This will result in:
#login-form .row:after{clear:both}
#login-form .row:before,#login-form .row:after{content:" ";display:table;}
#login-form .row:after{clear:both}
#login-form .col-md-7{position:relative;min-height:1px;padding-left:15px;padding-right:15px;float:left;width:58.333333333333336%}
#login-form .form-group{margin-bottom:15px}
#login-form .btn{display:inline-block;margin-bottom:0;font-weight:normal;text-align:center;vertical-align:middle;cursor:pointer;background-image:none;border:1px solid transparent;white-space:nowrap;padding:6px 12px;font-size:14px;line-height:1.428571429;border-radius:4px;-webkit-user-select:none;-moz-user-select:none;-ms-user-select:none;-o-user-select:none;user-select:none}#login-form .btn:focus{outline:thin dotted #333;outline:5px auto -webkit-focus-ring-color;outline-offset:-2px}
#login-form .btn:hover,#login-form .btn:focus{color:#333;text-decoration:none}
#login-form .btn:active,#login-form .btn.active{outline:0;background-image:none;-webkit-box-shadow:inset 0 3px 5px rgba(0,0,0,0.125);box-shadow:inset 0 3px 5px rgba(0,0,0,0.125)}
#login-form .btn.disabled,#login-form .btn[disabled],fieldset[disabled] #login-form .btn{cursor:not-allowed;pointer-events:none;opacity:.65;filter:alpha(opacity=65);-webkit-box-shadow:none;box-shadow:none}
#login-form .btn-primary{color:#fff;background-color:#428bca;border-color:#357ebd}#login-form .btn-primary:hover,#login-form .btn-primary:focus,#login-form .btn-primary:active,#login-form .btn-primary.active,.open .dropdown-toggle#login-form .btn-primary{color:#fff;background-color:#3276b1;border-color:#285e8e}
#login-form .btn-primary:active,#login-form .btn-primary.active,.open .dropdown-toggle#login-form .btn-primary{background-image:none}
#login-form .btn-primary.disabled,#login-form .btn-primary[disabled],fieldset[disabled] #login-form .btn-primary,#login-form .btn-primary.disabled:hover,#login-form .btn-primary[disabled]:hover,fieldset[disabled] #login-form .btn-primary:hover,#login-form .btn-primary.disabled:focus,#login-form .btn-primary[disabled]:focus,fieldset[disabled] #login-form .btn-primary:focus,#login-form .btn-primary.disabled:active,#login-form .btn-primary[disabled]:active,fieldset[disabled] #login-form .btn-primary:active,#login-form .btn-primary.disabled.active,#login-form .btn-primary[disabled].active,fieldset[disabled] #login-form .btn-primary.active{background-color:#428bca;border-color:#357ebd}
#login-form .form-control{display:block;width:100%;height:34px;padding:6px 12px;font-size:14px;line-height:1.428571429;color:#555;vertical-align:middle;background-color:#fff;background-image:none;border:1px solid #ccc;border-radius:4px;-webkit-box-shadow:inset 0 1px 1px rgba(0,0,0,0.075);box-shadow:inset 0 1px 1px rgba(0,0,0,0.075);-webkit-transition:border-color ease-in-out .15s, box-shadow ease-in-out .15s;transition:border-color ease-in-out .15s, box-shadow ease-in-out .15s}#login-form .form-control:-moz-placeholder{color:#999}
#login-form .form-control::-moz-placeholder{color:#999}
#login-form .form-control:-ms-input-placeholder{color:#999}
#login-form .form-control::-webkit-input-placeholder{color:#999}
#login-form .form-control:focus{border-color:#66afe9;outline:0;-webkit-box-shadow:inset 0 1px 1px rgba(0,0,0,.075), 0 0 8px rgba(102, 175, 233, 0.6);box-shadow:inset 0 1px 1px rgba(0,0,0,.075), 0 0 8px rgba(102, 175, 233, 0.6)}
#login-form .form-control[disabled],#login-form .form-control[readonly],fieldset[disabled] #login-form .form-control{cursor:not-allowed;background-color:#eee}
textarea#login-form .form-control{height:auto}
See this with your code: http://jsfiddle.net/gDraJ/
Note some less rules are wrapped in media queries (i don't know how to copy them). So in this example i use:
#login-form .col-md-7 {.col-md-7;
float: left;
width: percentage((7 / @grid-columns));
}
where #login-form .col-md-7 {.col-md-7;} should be expected.
In the fiddle example i also add:
#login-form
{
-webkit-box-sizing: content-box;
-moz-box-sizing: content-box;
box-sizing: content-box;
}
See: Twitter's Bootstrap 3 with ShareThis widget and Why did Bootstrap 3 switch to box-sizing: border-box?
update
In theory you also could wrap all content of bootstrap.less inside #login-form{}
and compile this. The resulting CSS will apply all Bootstrap's rules on #login-form only. Of course you could provide this CSS on an external url.