There are several ways to go, personally I’d just create a new subdomain dedicated to bitwarden (which appears to be what you want with https://bitwarden.example.tld/) then you can tell nginx to serve bitwarden when you access the website through this URL.
Roughly speaking I start my container like so:
docker run -d --name bitwarden -e WEBSOCKET_ENABLED=true -v /path/to/bitwarden/data:/data/ -p 127.0.0.1:1234:80 -p 127.0.0.1:3012:3012 bitwardenrs/server:latest
-p 127.0.0.1:1234:80 that rebinds the bitwarden’s 80 port to port 1234 in the host machine, and makes sure it only binds localhost so that it can’t be reached from the outside. That assumes of course that nginx will be running on the same machine.
Then you can configure your nginx as explained here, taking care to replace the
proxy_pass statements to use port 1234 instead of 80, and
<SERVER> should be 127.0.0.1: Proxy examples · dani-garcia/bitwarden_rs Wiki · GitHub (the “Nginx (by shauder)” one should do the trick).
Make sure to only allow HTTPS connections to the bitwarden instance. You can redirect HTTP to HTTPS with something like:
return 301 https://bitwarden.example.tld$request_uri;
I hope that helps.