When excited at sufficiently high acoustic pressures, a wall-attached bubble may exhibit asymmetric nonspherical modes. These vibration modes can be decomposed over the set of spherical harmonics Y_{nm}(θ,ϕ) for a degree n and order m. We experimentally capture the time-resolved dynamics of asymmetric bubble oscillations in a top-view configuration. A spatiotemporal modal analysis is performed and allowed recovering the set of zonal (m=0), tesseral (0<m<n), and sectoral (m=n) spherical harmonics that develop at the bubble interface. The analysis of the surface instability thresholds reveals that the frequencies of asymmetric modes differ from the standard Lamb spectrum. In addition, the nondegeneracy of asymmetric modes for a given degree n is evidenced by noncompletely overlapping resonance bands. Finally, the coexistence between zonal and sectoral modes is analyzed through their modal interaction, amplitude interplay and relation of phase, as well as their geometric compatibility.