I too noticed a large com.apple.bird file in the cache folder, tens of gigabytes.
Unchecking and checking iCloud preference did indeed reduced its size to less than 200Mb.
However after iCloud had finished downloading iCloud documents to my Mac, available disk space had been reduced by an amount approximately equal to the total size of documents.
Whereas that may make some sense, the available disk space was higher prior to unchecking and checking iCloud preference.
I was wondering whether an image or invisible copy of the downloaded documents resides somewhere in the system?
I have found the iCloud (archive) which is created after unchecking iCloud preference, and deleted it though it was not the culprit.
Any suggestions would be welcomed.