We need to know more in order to advise you much. Is that payment before or after taxes? Is the $3220 "down" your total drive off or just a capital cost reduction?
Where are you located? You should find a dealer who will deal with you in terms of invoice + markup. Often that is going to be the internet sales department and done via email.
That markup would be from $500-$1000 or so for a 3-series it seems. A 335 is tougher than a 328 in terms of the markup. But you should be able to get in that range.
Find the invoice cost from bmwconfig.com of the car you are considering.
You have a purchase price now to aim for. That should be further reduced by any incentives. Right now there is a $1000 incentive for the 3-series. If you already have a BMW there is a loyalty incentive as well of $750. These come off the negotiated price.
The only other fees are MACO (advertising, varies by region - in Los Angeles it is $380) and a minimal document fee.
If you set the price this way and then get buy MF and base acquisition fee, you will get a better deal than 90% of the people out there in the wild. Probably more.
This site and the other BMW boards are your friend. Read as much as you can in the order forum: