Update
Bootstrap now supports up/down keys as standard.
So if you want Tab to activate the dropdown, just get the key code (9) and do the following:
$('.input-group input').keydown(function(e){
if(e.which == 9){ // tab
e.preventDefault();
$(this).parent().find('.dropdown-toggle').click();
$(this).parent().find('.dropdown-menu a:first').focus();
}
});
And if you want to add further functionality for when the user is focused on a dropdown menu item:
$('.dropdown-menu a').keydown(function(e){
switch(e.which){
case 36: // home
e.preventDefault();
$(this).closest('.dropdown-menu').find('a:first').focus();
break;
case 35: // end
e.preventDefault();
$(this).closest('.dropdown-menu').find('a:last').focus();
break;
}
});
See this JSFiddle for a demo.