Magnetopolariton in bilayer graphene (BLG) is theoretically investigated with the consideration of the influence of asymmetry between on-site energies in the two layers of BLG. The results show that an ultrastrong light-matter coupling regime can be achieved in a high filling factor and asymmetry has a strong effect on it. Although BLG in the low-energy regime and semiconductor have a similar quadratic dispersion of quasiparticles, a remarkably different cavity quantum electrodynamics (QED) effect occurs in BLG. In particular, a quantum phase transition, as predicted by the Dicke model, occurs in BLG in spite of the Schrödinger-like term p2/2m in the system Hamiltonian, while such quantum phase transition does not exist in semiconductors. Most noticeably, the ultrastrong light-matter coupling can be easily controlled by modulating the asymmetry in BLG, which provides an excellent platform to observe interesting QED effects and can lead to tunable polariton-based devices and cavity-controlled magnetotransport in BLG.