You can use wp_dropdown_categories() to create your dropdown:
wp_dropdown_categories(array('taxonomy'=> 'post_tag','hide_empty' => 0, 'name' => 'my_tags'));
Update
the reason you are getting the term ID is because wp_dropdown_categories sets the ID’s as values so instead of just echo’ing it out you need to get the term, something like:
$term = get_term_by('id',$your_id,'post_tag');
echo $term->name;