The phrase 'to bend over backwards' for something or someone means to go to extraordinary lengths to make sure that thing happens or person gets what they want. ' Therefore, based on your above definitions, it's 1a: "the act or an instance of conceding". James is making a concession [he is conceding] to his boss because he is implying he is giving up something that he wants [free time, his weekend, a visit to a friend's], or working harder than he should have to.
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