If the bank and the website collude, they can de-anonymize attestation requests by correlating their two views of the interaction—the timestamps and various device fingerprints. It's impossible to make strong security guarantees against this threat model—imperfect statistical ones, at best.

Your version makes this trivial, since per your other comment, you expect the bank to insist on seeing the same IP address as the website, as an anti-fraud measure. ("If your IP doesn't match what you had at the bank, the RP rejects you.")