Usually the same or next day if there is no published routing between the two cities later in the day. WN doesn't go out of the way forcing same day routing for late bags, that's for sure.

I checked a bag late for an early coast to coast nonstop flight, WN's printed schedule showed 5 other flight routes/times between that early AM flight and the afternoon nonstop. The agent checking my bag (and the luggage assistance agent at origin) both said there was no point in me staying for the first of the connecting flights because it most likely would be held for the late evening nonstop. Still, I stayed at the airport for an hour when the scheduled 1-connection flight from my origin city arrived, and my bag wasn't on it. Doing so earned me a voucher since I picked up the bag the next morning saving them from shipping it