Declare an array at the start of your layout, or in your functions file depending on the scope required and populate the array with all the bands using get_posts and making the key the post ID.
You will then have a global array of bands, and can pull info from each one wherever you need it.
some similar code from something I worked on:
global $bands;
$bands = array();
$bandPosts = get_posts(array('numberposts' => -1, 'post_type' => 'lmfBand', 'order' => 'ASC', 'orderby' => 'title'));
foreach($bandPosts as $bandPost) {
$bands["{$bandPost->ID}"] = array($bandPost->post_title,$bandPost->post_name);
}
then to get the band name, just use: $bands[“{band_id}”][0] (in the version above)
You could also make each band a stdClass object instead of just an array of values.