Before you touch those screws, make sure the humidity is actually stable now - if it's still damp in there, you're just gonna be chasing the problem. Grab a moisture meter and check the drywall around that buckling area. If it's reading above 16-17% or so, you need to fix the moisture source first (seal that window, check for leaks, get some air flowing). Once things have dried out for a week or two, the drywall might actually flatten back on its own.
If it stays wavy after the humidity's under control, then yeah, you can screw it down without replacing the sheet. The pitfall nobody mentions: don't just go crazy with screws thinking more = better. Spacing them too close together can actually cause more problems down the road. Put new screws in every 12-16 inches in that bulging area, and here's the thing - use slightly longer screws than standard (maybe 1.5 inches instead of 1.25) so they actually bite into the stud and pull the sheet snug. Pre-drill slightly so you don't blow through the paper. Then spackle over the heads and sand smooth.
One more thing: check what's behind that wall. Window bays can have insulation issues or air gaps that trap moisture. Even after you fix the drywall, you might want to make sure there's nothing going on with ventilation or condensation buildup around the frame. A small vent or dehumidifier in the room during humid months could save you from dealing with this again next summer.