Every way is safe as long as you prepare for it :-)
But seriously, you have two main options
1) Do a database dump and restore to a bigger server. (the "logical
migration")
2) Stop the postgresql service, make a new filesystem on a bigger
device, move the database files there and mount the device under
/var/lib/postgresql. (the "physical migration").
I'm sure there are tons of howtos around the web since that's not
bareos-specific topic.
Of course if you move your database to a different server you'll have to
point the bareos director to the new server (update the config).
Best regards
MK