The offeror has stipulated that acceptance is to be by conduct
As explained in another answer, given that the offeror has stipulated that parking in the lot will constitute acceptance, and given that the offeror is master of the offer, then the question is whether the act of parking in the lot constitutes acceptance of the contract. I outlined the test in that other answer and will only summarize here: the question becomes "whether the offeror, acting reasonably, would understand that the offeree was assenting to the terms proposed." This is acceptance by conduct. This is an objective inquiry focusing on how the actions would be understood to a reasonable observer, not an inquiry into the actual states of mind of the offeror or offeree.
An example of the above law being applied can be found in University of Edinburgh v. Onifade, 2005 S.L.T. (Sh. Ct.) 63:
The pursuers' notice made it plain that their position was that anyone who parked on their property without a permit would have to pay them a fee of £30 per day on that account. The defender, by parking his vehicle on their property without a permit, made it plain that he accepted that position. He signified his acceptance by his conduct in so doing. It is nothing to the purpose for him to maintain that he did not intend to pay because he considered that the pursuers were not entitled to make the charge specified. 'The judicial task is not to discover the actual intentions of each party; it is to decide what each was reasonably entitled to conclude from the attitude of the other.'
See also Imperial Parking Canada Corporation v. Toronto (City), 2007 ONCA 649. The signs said:
Impark is by this sign offering space for public parking. You accept this offer by parking on this lot. Do not park on this lot if you do not agree to these terms and conditions … If you park and do not display a valid ticket or pass the rate is $69.55 per day or portion thereof.
The judge found:
the signs posted on Impark’s lots expressly state that Impark consents to the parking of cars without payment in advance and held that the fees that Impark collects are sums owing to it in contract rather than damages for trespass
In another parking lot example, Imperial Parking Ltd. v. Canada, 2000 CanLII 15612 (FCA), the Federal Court of Appeal said:
In my view, the unequivocal conduct which constitutes acceptance of the appellant's offer to provide a parking space occurs when the driver leaves the lot after parking his or her vehicle. This interpretation is reinforced by the text of the large sign posed at the entrance to the appellant's lot. That is the point in time in which an owner can be deemed to have accepted the appellant's offer. Any time before that moment, a driver can demonstrate his rejection of the appellant's offer by driving away. Those who purchase a ticket must be deemed to have accepted the appellant"s contractual terms upon leaving their parked vehicle in the appellant's lot. As for those who park their vehicles but fail to pay, the act of non-payment is more consistent with the intention to breach a contract than a refusal to enter into one.
Bob's sign/note/sticker is not likely an effective rejection of the offer
I understand you to be asking whether Bob's sign constitutes rejection of the offer such that Bob's subsequent conduct no longer would be considered acceptance of the contract.
A rejection would terminate the offer, such that it can no longer be accepted. However, rejection must be communicated to the offeror (Chitty on Contracts, § 4-124). In examples where apparent acceptance by conduct is negated by evidence of contrary intention, the offeror was in a position to be aware of the rejector's manifest expression of that contrary intention (see examples in Chitty on Contracts, § 4-035).