I have a 2 door 2009 Mini Cooper that has a weird intermittent problem. When I am idling – like at a stoplight – I hear a slight bump underneath the car. The sound is as if a mechanic has rolled under the car and sits up, banging his head on the undercarriage… every ten seconds… exactly. THE WEIRD THING, though, is that after I turn the car completely off, it will continue for roughly a minute and then finish off with 3 bumps. ba-dump-bump It’s all very soft but quite distinct. WHAT IS THAT??
You would probably have better chances at an answer, if you posted that Q. on a specialized Mini Forum.
There are plenty out there, I am sure…Google is your friend 
You have a 2009 Mini Cooper.
It is still covered by the factory warranty.
Take it to a dealer, and have them figure it out.
Then come back here and tell us what the cause was.
Where under the car is the bump coming from?
The center where the exhaust runs?
The back seat area, where the gas tank is?
Up front, where the engine is?
Left or right side of the car?
BC.
Since it is intermittent, of course it never “bumps” when I take it to the dealer. More than just “under the car,” it’s hard to pinpoint. If I were pressed, I would say center back.
This is just a WAG, but based on the supposed location of the noise, I am going to suggest that you consider the possibility that the evaporative emissions system is going thought its diagnostic self-test more often than it is supposed to.
I can tell you that on Toyotas, there is a fairly loud metallic noise underneath the car, in the general area of the driver’s seat, when the evap system goes through its self-test. This takes place when the car is left idle for an hour or more. If the Mini has a similar self-test of the evap system, and if it is being activated more often than necessary, that might explain this rhythmic noise that you are hearing.