Asked on Twitter to @Bitbucket
You can use the Bitbucket REST API to write your own script to retrieve the comments. First, you must make a request to retrieve the list of commits in the repository. Then you must make an additional request for each individual commit to retrieve any comments that are present on that commit. Please note, our API methods are paginated so you may have to make multiple requests to retrieve all of the commits and comments. (See the API documentation for more information).
https://confluence.atlassian.com/display/BITBUCKET/commits+or+commit+Resource#commitsorcommitResource-GETalistofcommitcomments
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