Admin-ajax.php appending a status code to ajax response

Put the die(); in your function:

add_action( 'wp_ajax_bubbly-upload', 'bubbly_upload_submit' );

function bubbly_upload_submit() {
    // generate the response
    $response = json_encode( array( 'success' => true ) );

    // response output
    header( "Content-Type: application/json" );
    echo $response;
    die();
}

Reference: WordPress Codex, AJAX in Plugins