No, ZoteroBib is entirely browser-based (stored in localStorage) so there is no server that would offer API to query. Optional persistence, i.e, "Link to this version" stores data used to produce bibliography as JSON server-side and offers no API.
Zotero translation server, which does a lot of the work behind ZBib (the part getting the metadata from URLs and other IDs), though, is accessible via API in a version hosted by the Wikimedia Foundation: https://en.wikipedia.org/api/rest_v1/#/Citation/getCitation
There'd be various option (either using other APIs or local tools) to process the returned metadata and get citations.
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https://en.wikipedia.org/api/rest_v1/#/Citation/getCitation
There'd be various option (either using other APIs or local tools) to process the returned metadata and get citations.