We discuss novel transverse plasmon polaritons that are hosted by AA-and AB-stacked bilayer graphene due to perfect nesting. They are composed of oscillating counterflow currents in between the layers, giving a clear interpretation of these collective modes as magnetic excitations carrying magnetic moments parallel to the planes. For AA-stacked bilayer graphene, these modes can reach zero frequency at the neutrality point and we thus predict a symmetry-broken ground state leading to in-plane orbital ferromagnetism. Even though it could be hard to detect them in real solid-state devices, these novel magnetic plasmons should be observable in artificial setups such as optical lattices. Also, our results might be relevant for magic angle twisted bilayer graphene samples, as their electronic properties are mostly determined by confined AA-stacked regions.