There's a weird combination of a few airlines sales at present that mean you can get to Bali for under a grand from almost every international airport in New Zealand (sorry, Dunedin, I tried my best!).
Summary:
Auckland - Bali (Denpasar) return (15 Oct 25 - 31 Aug 26) from $828 return
Christchurch - Bali (Denpasar) return (15 Oct 25 - 9 Mar 26) from $731 return
Dunedin - Bali (Denpasar) return (15 Oct 25 - 10 Aug 26) from $1109 return
Hamilton - Bali (Denpasar) return (15 Oct 25 - 12 May 26) from $865 return
Queenstown - Bali (Denpasar) return (15 Oct 25 - 30 Aug 26) from $935 return
Wellington - Bali (Denpasar) return (15 Oct 25 - 20 Mar 26) from $978 return
Flights are via Sydney, Melbourne, Brisbane or Gold Coast, generally.
Full list of flights I've found, and prices here.
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Warning: to get those rates you have to fly Jetstar (with no checked bags).