The tie will take place on Saturday 15th December with kick off at The Hive London at 3pm.
The Romans currently sit 6th in Vanarama National League South and knocked out Horsham with a 2-1 win in the last round.
Barnet and Bath have met before in the FA Trophy, back in 1969/70. The Bees overturned a 3-0 defecit to win 4-3 at Twerton Park.
Ticket details will be confirmed in due course.