Encrypt / decrypt with Ethereum wallet?

Let's say Alice wants to send Bob an encrypted message – both know each others' ETH addresses.

Alice writes a message, signs it with her private key, encrypts it using Bob's public key, and sends it to Bob.

Bob gets the message in his email and he uses his wallet to decrypt the message and verify that Alice signed it.

Is this general message sending possible with standard Ethereum wallets? I know that message signatures are common, but I haven't seen encrypted messages as much.

I know this should be possible if you have access to the raw private key but I'm hoping to be able to use hardware wallets for decryption as well.