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I have a very simple notebook, hosted on github and on bitbucket. The github URL displays fine in the nbviewer, but the bitbucket URL - which should indicate the same trivial notebook - does not work with the nbviewer.
Is it possible that nbviewer only takes github notebooks?
Later comment: my repo was private - so that was at least one reason why it could not work!
Based on this issue on Bitbucket's issue tracker, it does not seem to be supported yet.
Since this is/was the first result when googling for this, I just thought I'd update and let everyone know that this is now an add-on available in Bitbucket. You can find it under Settings -> Find Integrations. The source and issue tracker are available here - https://bitbucket.org/bitbucket/bitbucket-nbviewer
As pointed out by @ThomasK in the comments, you can display a notebook from bitbucket if you copy the raw address.
Just click on the three dots next to your notebook and copy the address that you get when you click on Open raw.
Copy this address...
... and paste it in the text box in https://nbviewer.jupyter.org/ ...
... and it will render your notebook: