What if Alice's offer can be accepted only by performance, by walking all the way across the bridge? Imagine Alice says, "I offer you $500 to walk across the Michigan Avenue bridge. You may accept only by walking all the way across the bridge."
The rule: If (1) an offer invites performance by acceptance, and (2) the offeree tenders or begins performance, then (3) an option contract is created. See Restatement (Second) Contracts ยง 45.
The existence of the option contract makes the offer irrevocable.