If the image proxy keeps served images cached for a period of time, bandwidth probably won’t be an issue. But if the image proxy queries the storage bucket every time someone accesses the image, egress charges will quickly add up.
Caching is up to the browser, so it's a per-user thing:
The image proxy isn't a caching proxy. Proxied images are never saved to disk, and only small chunks of images are stored in memory at any one time. The proxy does work with client-side caching (it passes on appropriate cache-related headers, etc.), so you may cache images.