For bugs, I'd expect a single commit to provide the fix; otherwise, the bug report needs splitting into multiple independent bugs. :)
Feature requests might require a whole branch, though. But in those cases, each individual commit in the branch would build towards the feature, and should reference the feature request.
From my experience, a bug can be simple to describe and atomic, but still require a significant amount of work to fix. I'm all for linking to bugs and feature requests in commit descriptions, but I wouldn't make it a hard requirement and put on the first line. Your mileage may vary.
Feature requests might require a whole branch, though. But in those cases, each individual commit in the branch would build towards the feature, and should reference the feature request.