Domain wall (DW) excitation spectrum for a bubble-state element has been investigated using three-dimensional micromagnetic simulations within a wide frequency range (0.1--100 GHz). Multiple DW resonance lines have been identified; localized modes at the DW in the low-frequency part of the spectrum and a set of high-frequency DW excitations above the frequency gap of domains spreading into the adjacent domains. In the last case, various DW modes with and without rotational symmetry coupled to multinodal domain modes are revealed. Due to the geometrical confinement leading to a strongly nonuniform static effective field, high-frequency DW modes with the same number of nodes but different localizations and frequencies exist, which prevents the use of a mode indexation with independent quantization numbers. The effects of the size of the element and a longitudinal polarizing magnetic field on the DW spectrum are then analyzed. In particular, the softening of the fundamental DW mode is evidenced at the first-order phase transitions between the bubble state and the saturated states. These numerical findings are discussed in light of theoretical models.