Use SearchWP's Supplemental Search Engine feature to limit search results to a single bbPress Forum

gistfile1.php

<?php

function myForumIncludeIds( $ids, $engine, $terms )
{
  if( $engine != 'my_forum_supplemental_engine' )
    return $ids;

  // set your forum ID
  $forumID = 900;

  // retrieve all of the Topic IDs for the Forum
  $topicsArgs = array(
    'nopaging'     => true,
    'post_parent'	 => $forumID,
    'post_type'    => bbp_get_topic_post_type(),
    'fields'       => 'ids'
  );
  $topicIDs = new WP_Query( $topicsArgs );

  // retrieve all of the Reply IDs from the Topics in the Forum
  $repliesArgs = array(
    'nopaging'        => true,
    'post_parent__in' => $topicIDs->posts,
    'post_type'       => bbp_get_reply_post_type(),
    'fields'          => 'ids'
  );

  $replyIDs = new WP_Query( $repliesArgs );

  // merge the two and use that as our limiter
  $includeIDs = array_merge( $topicIDs->posts, $replyIDs->posts );

  return $includeIDs;
}
 
add_filter( 'searchwp_include', 'myForumIncludeIds', 10, 3 );