Vault has a built in UI which does a reasonable job at allowing less technical people to update secrets. However Vault is very different from a user facing password tool like Bitwarden. While Vault is really a lower level database for secrets (where everything is centred around access to a specific secret and managing its lifecycle [especially if dynamically created]) Bitwarden is a lot higher level, with lots of business logic (password generation, metadata, sharing), integrations (browser plugins) and a very different threat design (Bitwarden is designed to prevent the server from seeing any secrets, while Vault is the opposite)
I guess the main question is what about Bitwarden are you liking that the basic Vault UI doesn’t provide? Does it matter for your users if a server admin could see all their secrets (which shouldn’t be possible for Bitwarden without having access to the user-held master password)?