If Alice has used a good, long, and complex passphrase then Bob will have to resort to brute force attack methods and put many GPUs or a botnet's power behind generating as many as possible passphrases and trying them until either thermal death of the universe or a matching passphrase had been found. For Alice, once losing her keyring, this becomes a gamble of how good her passphrase is vs how much computing cycles Bob has at his disposal.
If Bob has a friendly owner of a Crypto-coin mining farm then he maybe able to rent hashing time for mining passphrases instead of coins or if Bob managed to backdoor such a farm then he maybe able to employ significant computing power to generation of passphrases. Which may give Bob the required edge over Alice's security practices by throwing tons of attempts at her private key per second. Think of the infinite room of monkeys on typewriters that could have written Shakespeare if given enough time; more monkeys is more password attempts per interval of finite time measured.
If Bob lives in the future then according to lots of FUDers out there, all our crypto maybe at risk once quantum computers are reliable and cheap enough for state level actors to put a dedicated teem on. So if Bob has a friendly aunt Pam who works in a quantum server farm then all bets for Alice's passphrase keeping her docs secure are off.
Now if Alice has not used a passphrase or has used a weak passphrase then once her keys are in Bob's control, then Bob has effectively the permissions to be Alice; digital sex change... kinky.
As you've asked what that sort of attack would look like but my being to specific would be frowned upon, I'll leave you with one link that shows how to push a passphrase into GnuPG for automation and some key search terms; rainbow tables, john the ripper, dictionary attack. Try inputting any of those three in any combination with GnuPG and you'll likely find some teams working on testing/auditing passphrase security.
Note that password cracking software may not be designed with how GnuPG handles passphrases in mind. So if you're planning on testing your own key's security then you'll likely need to get creative with input/output between cracking software and GnuPG; hint understand the code linked above for input and output with GnuPG... as far as the passphrase cracking side, I can't offer any code examples on that subject publicly just yet.