You've got the process right. BMW will send them the app, they fill it out, get thier credit run, and then are approved. The whole deal can happen within a week or two.
I would argue against swapalease/leasetrader. Swapalease was expensive, and gave me almost no results. They also have terrible nagging salespeople that call constantly and try to upsell thier BS packages.
Try Craigslist first, I got 10x more hits than swapalease and ultimatley a sale.