This is not a bug per se -- but it's something that I desperately want.
I guess the Bitbucket "Inbox" is equivalent to Github notifications.
I want the inbox to show up very prominently on the "Blue bar" and NOT as a "menu item" (which it currently is). This is important because I don't want to have to remember to click the menu to know if there are any pending notifications -- I want notifications/messages to pop into my eye right away as soon as I log in.
This is what Github does -- I know you don't like hearing about your biggest rival -- but there are some things they do better -- and you can copy them (or may be implement them better).