(b) That's right. It is unlikely that A is bound by the 'terms and conditions' on the docket. The problem for B is that the docket is a 'non-contractual document', that is to say, a document that would not be expected to contain contractual terms. Because of this, it is not reasonable to expect A to read what is printed on the docket, or to assume that she assented to the terms, whatever they were. So unless terms are contained in a document that can reasonably be expected to contain contractual terms, they will not become part of the contract.
An exception is when terms in a non-contractual document are actually drawn to the attention of the other party, or a reasonable attempt is made to do so.