I see biting the bullet as accepting a claim in order to make your position consistent, while it undermines other beliefs that you want to hold, or decreases their credibility under your own standards. For example, when arguing about veganism someone may think the only way of resisting the pro-vegan conclusion is by accepting that the sheer membership to the human species confers someone the right to dispose of other animals in order to satisfy trivial needs like having a nice taste (I don't take a stand here on veganism, but I've seen such scenarios). But let's say the same person thinks that arbitrariness should be avoided as often as possible, but thinking the humans are so special for no independent reason is arbitrary. I think this qualifies as biting a bullet. Or suppose someone rejects the Anselmian ontological argument by denying that existence is a predicate, but the same person has some views about free model logic that require the existence as a predicate.
I see biting the bullet as accepting a claim in order to make your position consistent, while it undermines other beliefs that you want to hold, or decreases their credibility under your own standards. For example, when arguing about veganism someone may think the only way of resisting the pro-vegan conclusion is by accepting that the sheer membership to the human species confers someone the right to dispose of other animals in order to satisfy trivial needs like having a nice taste (I don't take a stand here on veganism, but I've seen such scenarios). But let's say the same person thinks that arbitrariness should be avoided as often as possible, but thinking the humans are so special for no independent reason is arbitrary. I think this qualifies as biting a bullet. Or suppose someone rejects the Anselmian ontological argument by denying that existence is a predicate, but the same person has some views about free model logic that require the existence as a predicate.