Had a simular experience happen to a friend (note different states have different laws so...).
She provided the dealership (it was a trade in too) with a bill of sale receipt and they took care of the title search and application.
If she was to sale this vehicle to a private citizen she would've had to go to the DOL and apply for a new title. To get this she would've had to provide the following info:
VIN, Year of vehicle, Model, make, where it was bought at (state, county etc..), where it was registered at and registration number (i.e. tag number). Then they would process it and it takes time.
Yes, dealing with the DMV or DOL (or whatever they call themselves in your state) can be fustrating and a lot of paper work, but some of it we bring upon ourselves (like losing a title :-) ). just be patient and if the dealer won't do it (which I'm sure they'll jump through the hoops because they want your business, especially now) do the paperwork and grin and bear it.