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.
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Action from Eastbourne Borough's visit to Bath City in National League South Photo: Lydia Redman:Lydia and Nick Redman
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Action from Eastbourne Borough's visit to Bath City in National League South Photo: Nick Redman:Lydia and Nick Redman
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Action from Eastbourne Borough's visit to Bath City in National League South Photo: Lydia Redman:Lydia and Nick Redman
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Action from Eastbourne Borough's visit to Bath City in National League South Photo: Lydia Redman:Lydia and Nick Redman