Have you not created a bit of a problem here, unless you have contacted the police to let them know the bike has been recovered?
If they see your wife riding around on a bike that matches your description, and they stop her and check the serial number, do you not consider that they will see her as the thief?
While it seems a great outcome, you should have left it the 72 hours with the police and kept them in touch with the bike's movements, and then left them to do the recovery.
Now, you could be headed for a potentially embarrassing situation and you could have some trouble explaining your way out of it because, technically, you have stolen back the bike, and especially as you obtained the serial number after the original theft (call evidence from this thread).
Machka's favourite bike was stolen from a campground, and every single detail was reported to the town's police, including the serial number and identifying photographs along with the description of what was a distinctive bike. The police dredged dams, put up fliers and all sorts of things in a small town. Nothing came of it.
Just over three years later, I saw the bike being offered on eBay in virtually complete and original condition save for some minor issues. We immediately put the matter in the hands of the police again, and co-operated with them to confirm the bike was Machka's, without taking it from the vendor. A court order was issued to enable the police to search the premises and seize the bike, which they did. Another court appearance was required to confirm the bike's identity and enable it to be returned to Machka. The person who had possession of the bike was not the thief, but someone caught in the crossfire.
From our experience, you have stepped entirely outside the process. It may have ramifications for you.