I think the story you're looking for is Against the Current by Robert Silverberg. It was first published in The Magazine of Fantasy & Science Fiction, October–November 2007.
Here's a summary:
A car salesman leaves work early after a sudden but short-lived migraine. As he makes his journey home he notices increasingly incongruous changes to the road and the neighbourhoods he drives through, until it becomes clear that he is in fact travelling through time. We follow his journey, as with Matheson’s Incredible Shrinking Man, as the salesman finds himself heading backward in time in ever increasing speed. He makes attempts to communicate with people he knew in times past, but this proves frustratingly problematic.
I recall a scene where he goes into a store to buy something, with his money from the future, and hopes that the clerk doesn't notice anything wrong. (IIRC, she doesn't.)
He stopped at the first motel on Lombard that had a vacancy sign and registered for a room. The price was only $75, but when he put two fifties down on the counter, the clerk, a pleasant, smiling Latino woman, gave him a pleasant smile and tapped her finger against the swirls of pink coloration next to President Grant's portrait. “Somebody has stuck you with some very funny bills, sir. But you know that I can’t take them. If you can pay by credit card, though, Visa, American Express—”
Of course she couldn’t take them. Rackman remembered, now, that all the paper money had changed five or ten years back, new designs, bigger portraits, distinctive patches of pink or blue ink on their front sides that had once been boringly monochromatic. And these bills of his had the tiny date “2004” in the corner.
I think he was driving on a bridge at some point.
At the Bay Bridge toll plaza they had taken down all the overhead signs that denoted the FasTrak lanes. That was odd, he thought.
he goes to meet up with a childhood friend of his when he reaches the time that they were kids.
Whatever had happened to old Al? Rackman had lost touch with him many years back. A powerful urge seized him now to drive across to Berkeley and look for him.
He might even have seen himself? I think he buys one of them - either the friend or himself - a drink.
No, neither of this happens. He agrees to have lunch with his friend though.
At the end, I believe that he just decides to keep driving and see what happens, coming to the conclusion that there's no way for him to reverse what had happened.
The story ends with:
He reached for the ignition key. Silently, smoothly, the Prius floated forward into the morning light and the night that would quickly follow it and into the random succession of springs and winters and autumns and summers beyond, forward into the mysteries, dark and dreadful and splendid, that lay before him.