10-using-custom-bulk-actions.php

<?php
add_filter( 'bulk_actions-edit-post', 'new_bulk_actions' );
function new_bulk_actions( $bulk_actions ) {
	$bulk_actions['send_by_email'] = __( 'Send By E-mail', 'text_domain' );
	return $bulk_actions;
}

add_filter( 'handle_bulk_actions-edit-post', 'new_bulk_action_handler', 10, 3 );
function new_bulk_action_handler( $redirect_to, $doaction, $post_ids ) {
	/* Exit if it's not send by email action */
	if ( 'send_by_email' !== $doaction ) {
		return $redirect_to;
	}
	/* Send e-mails */
	foreach ( $post_ids as $post_id ) {
		$current_user = wp_get_current_user();
		$current_post = get_post( $post_id );

		wp_mail(
			$current_user->user_email,
			$current_post->post_title,
			sprintf( '<a href="%1$s">%2$s</a>\n%3$s', 
				$current_post->guid,
				$current_post->post_title,
				$current_post->post_content
			)
		);
	}
	$redirect_to = add_query_arg( 'bulk_emailed_posts', count( $post_ids ), $redirect_to );
	return $redirect_to;
}