It’s easy. You only have to make a few modifications to the function get_bsearch_results in better-search.php
After the following line:
$output .= get_bsearch_header( $search_query, $numrows, $limit );
Add:
$search_query = preg_quote($search_query, '/');
$keys = explode(" ",$search_query);
Modify $output for $post_title as follows:
$post_title = get_the_title( $search->ID );
$post_title = preg_replace('/('.implode('|', $keys) .')/iu', '<span style="background:#ffc;"></span>', $post_title);
$output .= '<h2><a href="'.get_permalink( $search->ID ).'" rel="bookmark">'.$post_title.'</a></h2>';
Modify $output for the excerpt as follows:
$excerpt = get_bsearch_excerpt( $search->ID, $bsearch_settings['excerpt_length'] );
$excerpt = preg_replace('/('.implode('|', $keys) .')/iu', '<span style="background:#ffc;"></span>', $excerpt);
$output .= '<span class="bsearch_excerpt">' . $excerpt . '</span>';