Does anybody know how secure are my private repositories on bitbucket.org? Can I rely on that?
I have some repositories and I only want them to be reachable only by me and two others.
Well, it's certainly going to be available to bitbucket employees. Not that they'll be actively peeking into your code, but posting anything code in a SasS will, by definition, mean that your private data will not be absolutely private -- and subject to their security breaches, if any, on top of yours.
Well, ... so far I haven't heard of any incidents with BitBucket. So, I would say they are as private and as secure as any other of the kind (CodePlex, GitHub, et cetera et cetera).
In the end, as always, it always comes down to how much resources someone has to break into your private repository, and how much resources you're willing to invest to protect it. But I doubt that is your scenario, so I wouldn't worry about that.
If you really wish to ask about some specifics you can for example, find one of the authors of BitBucket on twitter Jesper Noehr.