Is there a way to get the bitrate of a specific region of a video?
You can only estimate the bitrate as proportion of your crop. If you have 30,000 Kbps for 1920*1080 pixel, then for 1080*1080 pixel this would mean 16,875 Kbps. If there is more complexity inside the crop region than outside, I would even increase the target bitrate further.

However, if your videos are not that long and not intended for streaming I wouldn't invest too much thought into saving some disk space. The video quality will degrade anyway with the encoding process and a high bitrate will help you avoiding too much loss.