How to add classes to the <li> tag in addition to the <ul> tag?

Woops, sorry about that - http://codex.wordpress.org/Function_Reference/wp_nav_menu

No worries, adding to the <ul> is easy, that can be done through the arguments you can pass when you call the wp_nav_menu function.

Something like

<?php
$args = array(
  'menu_class' => 'my-menu-class'
);

wp_nav_menu( $args );

Adding to the menu items is not as easy. As far as I know, the only way to do this would be with a custom walker class, which is not as easy to do. Look down a ways on that documentation, you'll see an example for Using a Custom Walker Function. That' allows you to rebuild the menu with the exact markup you want.

Which might be easier to change your js selectors to match the default classes bootstrap gives. That same documentation gives you all the classes in all the scenarios that menu gets, and I've found it's often easier to change your class selector.