Adam Murray’s side battled well but came home empty-handed and are still in the relegation zone.
They’ll look for better when they visit Truro – one of the sides they need to try to catch just outside the bottom four – next Saturday.
Get the Borough latest in the Herald – out on Friday – and check out Lydia and Nick Redman’s Bath City v Eastbourne Borough photos on this page and the ones linked.
1. Bath City v Eastbourne Borough pictures by Lydia and Nick Redman (27).jpg
Action from Eastbourne Borough's visit to Bath City in National League South Photo: Nick Redman:Lydia and Nick Redman
2. Bath City v Eastbourne Borough pictures by Lydia and Nick Redman (58).jpg
Action from Eastbourne Borough's visit to Bath City in National League South Photo: Lydia Redman:Lydia and Nick Redman
3. Bath City v Eastbourne Borough pictures by Lydia and Nick Redman (25).jpg
Action from Eastbourne Borough's visit to Bath City in National League South Photo: Nick Redman:Lydia and Nick Redman
4. Bath City v Eastbourne Borough pictures by Lydia and Nick Redman (9).jpg
Action from Eastbourne Borough's visit to Bath City in National League South Photo: Lydia Redman:Lydia and Nick Redman