Under ultrasonic excitation, bubbles in the liquid within a capillary can exhibit a variety of dynamical behaviors, including spherical oscillation, modal oscillation, and irregular surface oscillation. When a gas column is present in the capillary, the gas column and the capillary wall jointly constrain the bubble motion, leading to strong coupling between the translational motion and the radial oscillation of the bubble. An increase in the acoustic pressure amplitude modulates the distance between the bubble and the gas column, causing the bubble to gradually deviate from sphericity and display characteristic morphological evolution. By employing parameters such as circularity, modal dominance, and modal entropy, the bubble morphologies can be classified into three categories: spherical, regular, and irregular. Experimental observations reveal that fluctuations in the acoustic pressure modulate the onset of both stable modal vibration and modal instability in the bubble. In the case of stable modal vibration, the variation in bubble radius is governed by the radial vibration and the dominant mode; whereas under modal instability, the bubble exhibits pronounced non-dominant mode components. The third-order mode of the bubble predominantly occurs in regions relatively far from the gas column, while the fourth- and fifth-order modes are more frequently observed in the vicinity of the gas column. Under specific conditions, transitions between the fourth- and fifth-order modes can take place, indicating that the bubble morphology is jointly regulated by the gas column and the acoustic pressure. Theoretical analysis demonstrates that the presence of boundaries influences the nonlinear response of the bubble to a certain extent. When the bubble radius approaches approximately 51 μm, its sensitivity to acoustic field conditions and ambient pressure increases significantly. The acoustic pressure threshold for bubble modal excitation has been revised, and the theoretical threshold curve shows good agreement with the experimentally predicted threshold distribution. Within the transition region of the equilibrium radius distributions for bubbles of different modes, fluctuations in the acoustic pressure may excite switching of the bubble surface vibration mode between adjacent orders.