I've never seen a toll bridge that doesn't have tolls in both directions. I didn't even know that charging in only one direction was a thing. You live and you learn.
Fairly standard around Chicago area. Results for Illinois Tollway Plaza will show them (not all of them are - they can get interesting at intersections and off-ramps).
(late edit)
This is largely driven by the question "is a vehicle heading in one direction likely to return in the other?"
For trips from Oakland to SF, yes - it is very likely that the vehicle will go back across the bay bridge back to Oakland (rather than heading down to San Jose and then back up the other side).
On the other hand, a vehicle driving on the tollway through Chicago may be heading up to Minneapolis or to Detroit and then to other directions. Trips on the Illinois tollways are less likely to have a return trip and so both directions need to be tolled to capture the vehicles. It costs twice as much to do this (twice as many toll booths and staff) and so given the choice (trips to an island or other geographically isolated area) they only pay tolls in one direction.
Also tolls crossing into NYC. Since going around is impractical, it means you need half as much tolling. And since the land for tollbooths would be more expensive on the NYC side your savings are even larger.
Interesting! It may be a geographical thing. Clearly they don't want you to be able to do a free "circular commute" so for instance, in the Bay Area, all bridges charge toward San Francisco, and are free in the opposite direction. So there's no way to do a circular commute that wouldn't add 100+ miles by circumnavigating the Bay every day. But it seems like it "should" be simple enough (Dangerous words!) to coordinate say, "all bridges over a river in the metro area charge eastbound."
It seems kind of a waste from my perspective to have to do the traffic bottleneck in two directions.
An example: to use the ferry system here in Washington’s Puget Sound, you pay to go to the island, but the return trip is free. Same applies for bridges taking you to islands.
Here in the Bay Area all of our bridges only have tolls in one direction.