2011 Clubman S has what sounds like a bearing squeal on cold start. It goes away after about 1-2 min of driving and does not come back during the whole day. It happens really bad if the mini has sat for more than 1 day without moving. And only on first start up. Im trying to catch the problem before it gets bad and breaks something. Thank you!

 

Sounds like the oil pump noise at start up. The pump noise is very specific.Never heard it aside from this.

 

Possible belt squeal.

 

I'm New to the Mini Cooper scene so I can't say with any degree of certainty. The only thing I'm basing my opinion off of is 27 years of driving, and owning 30+ different cars. I would suggest the belt being warn. Easy way to rule it out is to buy some belt conditioner from the auto parts store. Apply it liberally while the car is running. You have enough access from behind the headlamp where the tensioner is. Apply it in the evening before you park the car for the evening. Then see what happens the next morning. I always try to eliminate the cheap and easy things first.

 

Perhaps we can separate a one time single " chirp" at cold start up from a loud squeal whether cold or on acceleration. When the timing chain is fresh and the newest tensioner installed AND proper oil level - you will hear a quick short " chirp" at startup. Its consistent and doesn't ever change its tone or duration. And it never occurs at any other time.

The above advice on the belt certainly applies to many cars. Especially those designs that use a V belt or more than 2 belts per pulley. The V fills with rust and condensation and makes a lot of noise. On our minis though that utilize a multi ribbed flat belt, I feel the dresser or lube will make matters worse and cause other troubles. The friction wheel for these belts is a smooth pulley, while the crank, AC and Alt are grooved. If the belt is encouraged to move "wide" against the smooth friction wheel it will get bound up and nicked in the housing that surrounds it. In short, the belts life will be shortened and will crack.
A new belt is cheap at 23 bucks. And while the friction wheel and swing arms are $160 ish-
when properly installed and " dry" the system works quite well is is very quiet.
Having been through many belts, friction wheels and other repairs over the years on these cars - I am confident in suggesting that you avoid belt " lube" or other dressings. If by chance you want to find out for yourself - disengage the friction wheel with the built in " pull tab" and start the car without tension on the belt. You will likely still hear a single "chirp" at cold start up - which is the oil pump.
Please let us all know what you find out in your investigation. I can post some pictures up in the AM of a used multi ribbed flat belt as well as the friction wheel with smooth pulley. You may better see what I am explaining above about the relationship of the belt and contact surface of the pulley.