I just checked tents and bivvy sacks at REI and they all flunk your cost requirement. This is probably the closest:
https://www.rei.com/product/203557/outdoor-research-alpine-ascentshell-bivyStill doesn't meet your cost criterion. Nor does the rest of their offerings.
Actually nothing works well in storm. The best I have done is a properly oriented rock shelter. A tarp at least is versatile - pitch it high or low, ridged or lean-to, just wrap yourself within, etc. They generally provide good ventilation and a superior view of your surrounding.
I do have tents but I am a tarp fan, especially when weight is critical.