it shouldn't be that bad if this is the optional audi parts that were fittted
if its an aftermarket set of parts then thats a different matter and it could well be specified incorrectly - one thing to check if it is a set of Koni's for example then these are usually adjustable in stiffness with a screw on the top or bottom of the shock
The first thing to do is check that the tyre pressures are correct to those stated in the manual , if this is OK then its also worth making sure that the suspension geometry is correct as if a camber or rear toe setting is out then this would make the car feel nervous,
I'd recommend taking the car to a place that does 4 wheel suspension alignment, most places use the back wheels as a datum and assume that they are perfectly straight and true. Often this is not the case and many modern cars are now adjustable at the rear as well as the front.
A 4 wheel alignment measures all four wheels independently and each is set -up without referring to each other and should only cost around £40.
If looks Ok then I'd consider fitting a taller profile tyre with a smaller diameter wheel, this will add some compliance to the ride and generally calm the quick responses. An alternative is to keep the current wheel and replace the tyres with some of a softer sidewallso removing some of the compliance in the system - Toyo's for example
This is especially true if you have run-flat tyres currently fitted
If you look on the tyre at the end of the number eris there's a letter the number just before this letter denotes the load capacity and therefore sidewall stiffness.
ie 225/55 R16 91V its the 91 you're interested in try a tyre with a lower figure and you'll get a softer tyre, however bear in mind this will also soften the steering response
Its also worth checking that all the main suspension pivot points have been tightened with the car on its wheels not in the air as this can add alot of friction to the suspension and lastly check that the brakes aren't binding at all as this too can make the ride very jerky and bouncy