There might be some bisync specific workaround others can point you into but in general in such situations the most obvious and cleanest solution is to utilize local file system snapshots.
I would wrap bisync command in script taking snapshot, running bisync against it and then deleting snapshot. Of course its feasibility depends on your local setup capabilities.
Personally I always use snapshots when running operations (backup, sync) that assume not changing state of data.
Below some simple overview and explanation:
https://cyounkins.medium.com/correct-backups-require-filesystem-snapshots-23062e2e7a15
Nowadays snapshots are available on all main OS - be it Windows, Linux or macOS - so really there is no excuse not to do it right:)