Yes, there’s a third party bridge available – see http://sourceforge.net/p/mrbs/feature-requests/160/
I use MRBS myself with Joomla 3, although I had to make a few modifications (see the SF link for details).
From: firstname.lastname@example.org [mailto:email@example.com]
Sent: 09 May 2014 04:38
Subject: [MRBS-general] Joomla 3 authentication
is it possible to authenticate in the mrbs with joomla 3 users?