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$first_char = 'B';

$postids=$wpdb->get_col($wpdb->prepare("
SELECT      ID
FROM        $wpdb->posts
WHERE       SUBSTR($wpdb->posts.post_title,1,1) = %s
ORDER BY    $wpdb->posts.post_title",$first_char)); 

if ($postids) {
$args=array(
  'post__in' => $postids,
  'post_type' => 'post',
  'post_status' => 'publish',
  'posts_per_page' => -1,
  'caller_get_posts'=> 1
);
$my_query = null;
$my_query = new WP_Query($args);