Using Drupal Bootstrap, I want the 'title' of my parent menu item to be a glyphicon and to drop to the search bar!
If you're wanting to theme the menu items, you can:


Use theme_menu_link() in your theme template to alter markup / attributes before rendering
Use a contrib module https://www.drupal.org/project/menu_attributes to add a custom class name e.g. icon-left icon-myname
Select the menu item via css and manually inject it there e.g.:

.menu-class .mid-class:before {
font-family: 'glyphicon';
content: '\utf-char-code';
/* other css here */
}



Adding the search block to the dropdown depends how you want to set this up, we'd need more specifics on what behaviour you're trying to achieve. Bear in mind that you can alter individual menu items through hooks in your template (e.g. theme_menu_link() above), and you can also render blocks programatically.