How to get post bulk edit action trigger and get edited post ids?

Question

I want to send email if a postmeta of a post is changed to the expected value.So previously i was doing loop to check the post meta in each post. In here am running the loop in admin_init hook. But this slow down the site, so i'm thinking to do this on save post only. SO the edited post may have the meta value am expecting then i'll send the mail.

Previous

$the_query = new WP_Query( $args );
if ( $the_query->have_posts() ) {

    while ( $the_query->have_posts() ) {
        $the_query->the_post();
        if(get_post_meta($the_query->post->ID,'custom_post_meta',true)=='ok'){
        //mail() function goes here
        }
    }

} 

wp_reset_postdata();

This is unwanted because only certain post may be edited. Blindly checking post meta with a loop every time is waste.

So i thought to use on save_post on save we'll check whether the post meta is changed to the expected value then we'll do the mail.like below

function testing($post_id){
    if(get_post_meta($the_query->post->ID,'send_mail',true)=='ok'){
        //mail() function goes here
        }
        //only for edited post alone i'm checking here
}

add_action('save_post','testing');

There are another two scenario where the post meta may be changed which are bulk edit and quick edit

For quick edit i found this

function check(){
var_dump($_REQUEST);//can able to get the post id, i can do the rest
}
add_action('check_ajax_referer','check');

But for bulk edit i don't have any clue. I tried searching, In this answer i found that $_REQUEST may contain action and postid. So i thought for bulk edit there might be an action in $_REQUEST['action'] but i couldn't find when i try like this

function another_check(){
var_dump($REQUEST['action']);
}

add_action('admin_init','another_check');

I found this check_admin_referer too but i couldn't able to figure out as it does not print when i var dump. Will this(check_admin_referer) work or suit on this? Is there any other easy way to get the edited post ids?

How can i get the List of post id on bulk edit? From then i can able to do the check and send mail accordingly