Yes, it does. The integration with both Safari and Firefox on iOS is excellent. In Settings -> Passwords & Accounts -> Autofill Passwords you just change the backend from iCloud Keychain to Bitwarden, then it otherwise behaves substantially the same.

A big benefit of switching to Bitwarden is that you can also get it up and running on non-Apple machines. Kicking myself for not doing it earlier.

Just be aware that bulk exporting your passwords from iCloud Keychain is non-trivial.