BuddyPress.org

@balkanpeople
1. create a child theme of bp-default theme
2. copy header.php and sidebar.php from bp-default theme to your child theme folder
3. Copy line 84 through line 102 of header.php to your sidebar.php wherever you want it to appear and save sidebar.php
https://trac.buddypress.org/browser/tags/1.2.5.2/bp-themes/bp-default/header.php#L84
4. Delete search code you copied to sidebar from header.php