7 - Sorting a Views exposed filter options alphabetically
J. Reynolds suggestion was the answer. 

Creating a new function for the sort code and using $form['#after_build'] to call it resulted in the select box being sorted alphabetically.

function dependant_keyword_filter_form_views_exposed_form_alter(&amp;$form, &amp;$form_state){
if ($form['#id'] == 'views-exposed-form-annotated-bibliography-page') {
    $form['#after_build'][] = '_sort_alphabetically';
  }
}
function _sort_alphabetically($form, $form_state) {
        foreach ($form_state['view']-&gt;filter as $field =&gt; $filter) {
            if ($filter-&gt;options['exposed']  &amp;&amp; $filter-&gt;options['id'] == 'field_keywords_tid' ) {
                $field_id = $form['#info']["filter-field_keywords_tid"]['value'];
                asort($form[$field_id]['#options']);
            }
        }
        return $form;
}