You can deploy Bamboo with HAProxy on each Mesos slave. Each web service being allocated on Mesos Slave can discover services via localhost or domain you assigned by ACL rules. Alternatively, you can deploy Bamboo and HAProxy on separate instances, which means you need to loadbalance HAProxy cluster.
UI is useful to manage and visualize current state of proxy rules. Of course, you can configure HAProxy template to load balance Bamboo.