I believe the datepicker is more of a jQuery UI component. So I think you just need to add that script to your project. Just so you know the Developers of Bootstrap, not the BSS app, have a warning http://getbootstrap.com/javascript/#js-events
Third-party libraries
Bootstrap does not officially support third-party JavaScript libraries like Prototype or jQuery UI. Despite .noConflict and namespaced events, there may be compatibility problems that you need to fix on your own.
In my current project I do use jQueryUI and I'm not seeing a problem with it, however, it may possible I'm not using the plugin that could be an issue.