If you want to execute the same snippet of code, you might refactor it into a separate function, and call it from both `mymodule_form_submit` and `mymodule_cron`. Something like the following:

    function _mymodule_set_expiry_date() {
      db_insert('bds_user_expiry')->fields(array(
        'uid' =>$user_id,
        'active_user'=>strtotime("now"),
      ))->execute();
      drupal_set_message(t('You have successfully set the expiry date'));
    }

And then, on your hooks:

    function mymodule_form_submit($form, $form_state) {
      _mymodule_set_expiry_date();
      // ... rest of your code
    }

    function mymodule_cron() {
      _mymodule_set_expiry_date();
      // ... rest of your code
    }


You can see the following question on Drupal Answers for a more detailed explanation about `hook_cron` and `hook_cron_queue_info`: https://drupal.stackexchange.com/questions/69332/how-to-use-hook-cron-queue-info-in-a-custom-module 

Hope that helps,