(b) That's right. There is probably insufficient agreement for A's promise to be enforced. Although A has said he will pay a bonus, he has not said when he will pay it or how much it would be. The whole matter is left pretty much to his own discretion. When the content or extent of something promised is left to the discretion of the promisor, the promise may be illusory because on analysis nothing of substance has been agreed and the apparent promise cannot be enforced.
This does not mean that every promise must be expressed in exact detail or in exactly measurable terms to be enforceable. The courts will do their best to give effect to what has been agreed, even if the contract is open to different interpretation. In particular, a court can take account of relevant industry standards, or past dealings between the parties, to ascertain details not expressly included in the agreement.