Thats what we call "the Shimmy", as JB has said worn front suspension parts, which one ?? hard to say....
Getting rid of the shimmies
Once all the easy options are out of the way, tyres ,tracking and wheel balance, we have to move on to the front suspension components. There is a lot of advice given on what to change first but in my experience most problems are either removed entirely or at least made significantly better by replacing the upper arms and rubber bushes.
While you are at it you might as well replace the lower arms as well, the cost is not all that high and is worth doing once the car is on the lift. A big difference can be made by just changing the bushes but normally if the bushes are damaged then the ball-joints are damaged at the same time. The deterioration of the bushes is often missed, the weight of the car on these parts makes it difficult to find with a crow-bar so don't be surprised if the garage tells you they can't find any play. Some like to replace the bushes with polyurethane after-market versions, be aware though that this will significantly affect the quality of the ride and may well lead to other component failures. The bushes have to be pressed into the arms if you buy them separately.
Getting rid of shimmies - it's getting much harder now
We have now covered the possible causes in 95% of the cases I've been involved with. I have heard of miracle fixes where just one component of the front suspension has been replaced before the usual things have been tried but these are really just one-offs. So, in order of the most likely here are the remaining candidates:
Front stabiliser joints.
Centre tie-rod, Drag link bearing and Tie rods.
Once you have got to this point things have got pretty expensive. You can get complete suspension refurbishment kits from Ebay.de, I have never tried these but have heard good things about them. Unfortunately, as you have just bought your car that has shimmy you will not be aware of what has been changed already.
Hope this helps a bit, you can find all the part #'s etc at: RealOEM.com Online BMW Parts Catalog