Bamboo "Load Repositories" breaks with Bitbucket 2 factor auth

When connected to a Bitbucket with 2FA enabled, the following error is thrown when trying to Load Repositories:

Failed to load data from Bitbucket. com.atlassian.bamboo.plugins.hg.bitbucket.api.BitbucketApiException: {"error": {"message": "Resource not found", "detail": "There is no API hosted at this URL.\n\nFor information about our API's, please refer to the documentation at: https://confluence.atlassian.com/x/IYBGDQ"}}

Issue only happens when using BitBucket type repositories and trying to load the list of repositories. Specifying a clone URL manually works normally.

Workaround

Use Git type repository instead and define the clone URL through SSH or HTTPS.