The car is real, it still runs, and it's mostly original/unrestored.
It ended up in the hands of a private owner in the midwest a couple years after the movie. (McQueen himself offered to buy it back at one point but the owner wouldn't sell.) Its location was always known by a few insiders but it was never made public. The owner/family finally decided to take it out of hiding & sell it recently.
Other Bullitt cars -
There were two of each car, 1 stunt car and 1 closeup (or 'hero car').
This thread is about the hero Mustang.
The stunt Mustang was long thought to be scrapped until it was recently found in Mexico. It was rougher than the hero Mustang but still restorable.
The stunt Charger was said to have been crushed/scrapped right after filming. It had gotten pretty thrashed by the end of the chase.
The hero Charger is not officially found. Unofficially, there is a strong contender with circumstantial evidence. (Ford was a big product-placement supplier to Hollywood in that era and kept records. But the Bullitt crew bought the Dodges at a local dealership and the VINs are not known.)
