We study the role of anisotropic escape in generating the elliptic flow of bottomonia produced in ultrarelativistic heavy-ion collisions. We implement temperature-dependent decay widths for the various bottomonium states to calculate their survival probability when traversing through the anisotropic hot medium formed in noncentral collisions. We employ the recently developed <math><mrow><mn>3</mn><mo>+</mo><mn>1</mn></mrow></math>-dimensional quasiparticle anisotropic hydrodynamic simulation to model the space-time evolution of the quark-gluon plasma. We provide a quantitative prediction for the transverse momentum dependence of bottomonium elliptic flow and the nuclear modification factor for <math><mrow><mi>Pb</mi><mspace width="0.16em"></mspace><mo>+</mo><mspace width="0.16em"></mspace><mi>Pb</mi></mrow></math> collisions in <math><mrow><msqrt><msub><mi>s</mi><mi>NN</mi></msub></msqrt><mo>=</mo><mn>2.76</mn></mrow></math> TeV at the CERN Large Hadron Collider.