Bugzilla has a number of APIs that you can call in your code to extract information from and put information into Bugzilla. Some are deprecated and will soon be removed. Which one to use? Short answer: the REST WebService API v1 should be used for all new integrations, but keep an eye out for version 2, coming soon.
The APIs currently available are as follows:
4.6.1. Ad-Hoc APIs¶
Various pages on Bugzilla are available in machine-parsable formats as well as HTML. For example, bugs can be downloaded as XML, and buglists as CSV. CSV is useful for spreadsheet import. There should be links on the HTML page to alternate data formats where they are available.
Bugzilla has a REST API which is the currently-recommended API for integrating with Bugzilla. The current REST API is version 1. It is stable, and so will not be changed in a backwardly-incompatible way.
This is the currently-recommended API for new development.
This documentation undoubtedly has bugs; if you find some, please file them here.