Bitwarden is cloud-based with synchronization to local caches. If you want total control over your data with Bitwarden you will need to run the server/cloud side. I'd caution that running a Bitwarden server is not for everyone, as one could make the security worse than the Bitwarden-company-hosted cloud service.

I run Vaultwarden on my LAN, with no public/Internet facing service, and sync only on my LAN.