how to bulk add one line in the first paragraph of all posts

I’d go for solution posted by @butlerblog – it’s a lot easier to manage and change in the future and it’s better WP practice.

But… If you’re asking… Here are the ways you can do this:

1. WP way:

function prepend_content_to_posts() {
    $to_prepend = 'This will be prepended';

    $posts = get_posts( array( 'posts_per_page' => -1 ) );
    foreach ( $posts as $post ) {
        wp_update_post( array(
            'ID' => $post->ID,
            'post_content' => $to_prepend . $post->post_content
        ) );
    }
}

Then you’ll have to call that function. Be careful not to call it twice – it will add your content twice in such case.

2. MySQL way:

UPDATE wp_posts
    SET post_content = CONCAT('<YOUR STRING TO PREPEND>', post_content) 
    WHERE post_type="post" AND post_status="publish"

Be careful to change table prefix according to your config.