Even though Firefox does not support U2F by default, there's a [working U2F plugin|https://addons.mozilla.org/en-US/firefox/addon/u2f-support-add-on/?src=api] that works well (tested with Github and Google), but Bitbucket won't even allow the use of U2F if it does not see Google Chrome, and prints this message instead:
"Your browser doesn’t support the FIDO U2F standard yet. Get the latest version of [Google Chrome|https://www.google.com/chrome/browser/desktop/] if you want to use a security key device"
It's a shame this is based merely on User Agent and not the actual capability of browser, which can obviously be extended with a plugin.
Attached are two screenshots: one from Chromium demonstrating correct behavior; and one from Firefox showing the error.