How can you integrate BAPI in SAP Process Integration with a 3rd party?

You can import the BAPI in SAP PI Enterprise Service Repository (ESR) and create an interface using that. Then you can create an integrated configuration in SAP PI Integration Directory (ID) using the interface and get WSDL URL.

You can provide the WSDL URL to the third-party system. Now you successfully exposed the BAPI as a SOAP web service to the third-party system.