You are in control here. It's like every other bit of software you run yourself: it's your problem to do it properly.
1) if you worry about people replacing the docker image you are using, build your own. It's not hard. Alternatively, use a specific version of the docker image by specifying the version or the hash (if you are really paranoid). Of course after you review the Dockerfile. Minimum at least glance through the Dockerfile.
2) bitwarden has import/export functionality (client side) so if your server disappears for whatever reason, you can still export your passwords from the client side.
3) if you don't trust the OSS code, audit it or at least look through it. That's the whole point of OSS. Build it from source if you must. File bugs. Look at the issue tracker. You can choose not to but if something happens it's your problem; not somebody else's problem.
4) The vault is encrypted and the server never handles or sees the decrypted content (see 3 to verify this). Other people's ability to break that encryption depends on you using a secure master password.
5) Or just pay Bitwarden to host passwords for you and rely on their terms of use, SLAs, support, good reputation, and what not. That's probably the best option if you want ass coverage for professional usage. Their pricing is very reasonable for small setups. And probably sharing passwords with a large group of users is just a spectacularly bad idea to begin with. A couple of key users, should cost you max 20/month. Not really worth dedicating devops time for self hosting unless you have a really good reason to. If you do, see 1-4.