this is more of a suggestion than an answer. I’m not an expert on custom post type pagination, or custom post types, but I’ve spent quite a bit of time testing different methods. I’ve found one that works pretty good and doesn’t require a plugin. I still keep up with this subject on various websites, but for now this is working for me. If your interested here is the link to the source:
Custom Post Type Pagination Chaining Method
REVISION:
If you don’t want to mess with the method above I have a possible solution that is closer to what you’re currently using. Here is my version of the code you posted:
<?php $paged = ( get_query_var( 'paged' ) ) ? get_query_var( 'paged' ) : 1; ?>
<?php $offset = ( 1 * $paged ) - 1; ?>
<?php $args=array(
'paged'=>$paged,
'posts_per_page'=>1,
'post_type'=>'bingo_review',
'offset' => $offset);
?>
<?php query_posts($args); ?>
<?php if(have_posts()) : ?><?php while(have_posts()) : the_post(); ?>
blah
<?php endwhile; ?>
<?php endif; ?>
<?php wp_paginate(); ?>
Give that a try and let me know how it turns out.