If the bibtex citation is in the metadata of the publication item, you can do a GET item call to obtain the citation in the XML/JSON metadata.
Bear in mind that in order for you to obtain the bibtex citation, you would have to do a GET call to the specific item (/work/PUT-CODE) and not the work sections in general (/works). If you do a GET /works call, you will get a summarized response of all the work items of that record. This summarized response does not contain the bibtex citation.
<common:created-date>2022-04-10T12:53:45.064Z</common:created-date>
<common:last-modified-date>2022-04-10T12:53:45.064Z</common:last-modified-date>
<common:source>
<common:source-client-id>
<common:uri>
https://orcid.org/0000-0002-XXXX-XXXX</common:uri>
<common:path>0000-0002-XXXX-XXXX</common:path>
<common:host>
orcid.org</common:host>
</common:source-client-id>
<common:source-name>Europe PubMed Central</common:source-name>
<common:assertion-origin-orcid>
<common:uri>
https://orcid.org/client/0000-0002-XXXX-XXXX</common:uri>
<common:path>0000-0003-XXXX-XXXX</common:path>
<common:host>
orcid.org</common:host>
</common:assertion-origin-orcid>
<common:assertion-origin-name>John Doe</common:assertion-origin-name>
</common:source>
<work:title>
<common:title>Work Title</common:title>
</work:title>
<work:journal-title>Journal Title</work:journal-title>
<work:citation>
<work:citation-type>bibtex</work:citation-type>
<work:citation-value>@article{PMID:12345,
title = {This is the Work Title.},
author = {Author One, Author Two},
doi = {10.12345/s1234},
journal = {This is the Journal Title},
month = {04},
year = {2022}
}</work:citation-value> </work:citation>
<work:type>journal-article</work:type>
<common:publication-date>
<common:year>2022</common:year>
<common:month>04</common:month>
</common:publication-date>
<common:external-ids>
<common:external-id>
<common:external-id-type>pmid</common:external-id-type>
<common:external-id-value>12345</common:external-id-value>
<common:external-id-normalized transient="true">12345</common:external-id-normalized>
<common:external-id-relationship>self</common:external-id-relationship>
</common:external-id>
<common:external-id>
<common:external-id-type>doi</common:external-id-type>
<common:external-id-value>10.12345/s1234</common:external-id-value>
<common:external-id-normalized transient="true">10.12345/s1234</common:external-id-normalized>
<common:external-id-url>
https://doi.org/10.12345/s1234</common:external-id-url>
<common:external-id-relationship>self</common:external-id-relationship>
</common:external-id>
</common:external-ids>
<common:url>
http://europepmc.org/abstract/med/12345</common:url>
<work:contributors>
<work:contributor>
<work:credit-name>Contributor One</work:credit-name>
<work:contributor-attributes>
<work:contributor-sequence>first</work:contributor-sequence>
<work:contributor-role>author</work:contributor-role>
</work:contributor-attributes>
</work:contributor>
<work:contributor>
<work:credit-name>Contributor Two</work:credit-name>
<work:contributor-attributes>
<work:contributor-sequence>first</work:contributor-sequence>
<work:contributor-role>author</work:contributor-role>
</work:contributor-attributes>
</work:contributor>
<work:contributor>
<work:credit-name>Contributor Three</work:credit-name>
<work:contributor-attributes>
<work:contributor-sequence>first</work:contributor-sequence>
<work:contributor-role>author</work:contributor-role>
</work:contributor-attributes>
</work:contributor>
</work:contributors>
</work:work>