I am developing a web application in which I need to encrypt sensitive information. My plan is to use use AES-256 where the private key is encrypted by a hash of the user's password. I need to store the hash of the password for authentication purposes, but it obviously can't be same used to encrypt the private key. My current thought is to use bcrypt to generate a key to be used to encrypt the private key. For authentication, my thought was to simply hash the password using bcrypt and then hash that hash using bcrypt again and then store that hash in the database. Since it is one way, there shouldn't be any way to use the stored hash to decrypt the private key? Are there any obvious security issues with doing this that I may be missing?

My other thought was to use two different encryption algorithms, such as using a bcrypt hash to encrypt the private key and storing a SHA-2 hash for authentication purposes.

Thanks for your help.