What problem is it causing?

The International Residential Code, which forms the core of most states' statewide building codes, permits the use of stud cavities as air returns, provided they meet a number of conditions (see section M1601.1.1) It appears to me that the stud cavity shown in the photo does not have the required fire blocking. I'd also be concerned about pulling moisture from the bathroom into the return which can be prevented with proper air sealing. All of that could have been accomplished from the bathroom side of the wall prior to installing the shower. Unless the shower can be easily moved, you're going to need "surgery" to be performed from the bedroom side.

Your contractor has an obligation to meet local code requirements. Doing so in this case should not result in an opportunity to pick your pocket. I suggest they record any expenses as "contractor continuing education."

I think it could work satisfactorily if you do the following:

Measure the inside distance between the two studs (should be around 14 1/2"), and the distance between the narrow side of the studs facing the bathroom and the shower stall, minus 1/8" to 3/16". Cut a piece of drywall as tall as you can maneuver through the opening on the bedroom side, and as wide as the outside distance between the studs (should be around 17 1/2"). screw two pieces of 2x2 or the like to the drywall, 14 1/2" apart (or the exact measured distance between the studs). Cut another piece of drywall having its width equal to the distance between the studs and the shower stall, minus 1/8" to 3/16" to allow for thermal expansion of the shower walls, and its length equal to the length of the other drywall piece, or a bit smaller. Fix that second piece perpendicular to the other drywall piece, in a manner to form a little "shelf" atop the first piece.

Maneuver the piece between the studs, as high as you can go while still being able to screw the pieces of 2x2 to the studs. If you still have a gap, cut another piece of drywall, screw two cleats spread apart the inside width between the studs, maneuver it below the first piece, and screw to the studs.

This won't create a 100% airtight seal, but il will block most of the airflow.

Perhaps someone will have a better solution.

The OP shouldn't need to do more than point out that the current installation fails to meet code. If the OP prescribes a fix or implements one on their own, then they "own" the solution--which may not function as intended or meet code requirements.

If the contractor can't figure it out, I'd invite the local code official to have a look. If the shower was added without a permit, that will make things even more interesting.

You've left several questions unanswered before meaningful advice can be given. Rather than chase it around here I recommend you do as CR Homes suggested.

Thank you for the detailed and thoughtful guidance. Much appreciated!