No, stops instantly
As @Threevok sounds more like a seatpost issue than a BB issue, as standing up would be less likely to make it go away there than if it's the seatpost.
No, stops instantly
Have you cleaned inside of seat tube? Sometimes minute particles of grit get down there and it can be very noisy especially if you have an aluminium frame.
Are you being followed everywhere by a crocodile that once swallowed an alarm clock?