BuddyPress.org

In case others are curious here’s what I did:

I copied the function bp_get_nav removed the lines with the logout link and renamed it to bp_get_nav_no_logout as suggested above by jjj. Then I put this newly created function in the functions.php file in my theme and I changed the userbar.php file to call bp_get_nav_no_logout.

That way I keep it with my custom theme and leave the core files untouched.

Thanks again John.