Use the cssrewrite
filter provided by Assetic to correct the paths within your CSS files.
{% stylesheets filter='cssrewrite'
'bundles/myassetbundle/css/bootstrap.min.css' %}
<link rel="stylesheet" href="{{ asset_url }}" />
{% endstylesheets %}
Make sure that you are using the bundles/myassetbundle/...
notation instead of the @MyAssetBundle
one.
Read the Symfony docs about this matter.