Just providing a connection string wouldn't be enough; EntLib requires the provider name too to determine both the ADO.NET provider factory to use and the Database type that provides the customized behavior.
It's far from ideal, but you can use a DatabaseProviderFactory with a dictionary configuration source like this:
DictionaryConfigurationSource source = new
ConnectionStringsSection section = new
@"Data Source=.\sqlexpress;Initial Catalog=Northwind;Integrated Security=True",
DatabaseProviderFactory factory = new
Database db = factory.Create("connection string");
Of course, this isn't much better than what you had initially (although you could use OleDbFactory.Instance to get the DbProviderFactory instead of going through the DbProviderFactories class and get rid of some clutter.)