The BEDB.BAk holds all the info about your tape/B2D volumes, jobs, schedules, select lists etc, so you definitely need this
You also need the catalog directory, or you will need to inventory and catalog any tape you want to restore from a rather laborious process if you have a large number of tapes
and the log files are nice to have, but not essential.
http://seer.entsupport.symantec.com/docs/319367.htm contains directions to re-install Backup Exec, but if you have backups/saved copies of all the stuff they say to move to a temp storage location, you should be good to go