Resurrecting this ancient post of mine to say that I finally figured this out. The problem was that my internal certificate on the Bitwarden server had a validity period of several years. When I read an article about the time limitations Apple imposed in iOS for certificates, it clicked that this might be the problem even though the errors I was getting were seemingly unrelated.
Sure enough, I changed the cert to one with a 1 year expiration and the app works fine on my iPhone now.
Just posting this in case anyone else stumbles across this post after seeing the same kind of errors. I still don't like that Apple arbitrarily imposed this limit on my own device with my own server and my own CA, but it's easy enough to work around.