What is the edmunds.com price for the same spec car if u try the "appraise my car", as if u were going to sell the car to the dealership. Then aim for that price as your target. If the car sales guy won't budge... Tell him u are working on a private seller as well and you want to see how that goes because that guy is motivated to make the sale now.
Tell the dealership guy to hang on to your number and give u a call when the numbers can work (hopefully you will still be on the market for a car when he's read to sell). So basically by saying this you have flipped it to the bmw salesman is not willing to sell you the car and he can just keep his parking lot growing and no commission. He will call u in a couple days and thats when you have to say "the private party guy is ready to get a ppi done on the car with me on the weekend, has anything changed on your side mr salesman? Let me know if your ready to sell because i'm about to pull the trigger on another car". That will light the fire u need.