Motivated by recent experiments, we model the dynamics of bright solitons formed by cold gases in quasi-1D traps. A dynamical variational Ansatz captures the far-from-equilibrium excitations of these solitons. Due to a separation of scales, the radial and axial modes decouple, allowing for closed-form approximations for the dynamics. We explore how soliton dynamics influence atom loss and find that the time-averaged loss is largely insensitive to the degree of excitation. The variational approach enables us to perform high precision calculations of the critical atom number (i.e., the maximum number of atoms that can exist in a single soliton before the attractive forces overwhelm quantum pressure, leading to collapse). © 2019 American Physical Society.