Fish outperform current underwater robots in speed, agility, and efficiency of locomotion, in part due to their flexible appendages that are capable of rich combinations of modes of motion. In fish-like robots, actuating many different modes of oscillation of tails or fins can become a challenge. This paper presents a highly underactuated (with a single actuator) fish-like robot with a bistable tail that features a double-well elastic potential. Oscillations of such a tail depend on the frequency and amplitude of excitation, and tuning the frequency-amplitude can produce controllable oscillations in different modes leading to different gaits of the robot. This robot design is inspired by recent work on underactuated flexible swimming robots driven by a single rotor. The oscillations of the rotor can propel and steer the robot, but saturation of the rotor makes performing long turns challenging. This paper demonstrates that by adding geometric bistability to the flexible tail, turns can be performed by controllably exciting single-well oscillations in the tail, while exciting double-well oscillations of the tail produces average straight-line motion. The findings of this paper go beyond the application to a narrow class of fish-like robots. More broadly we have demonstrated the use of periodic excitation to produce bistable response that generate different gaits including a steering gait. The mechanics demonstrated here show the feasibility of applications to other mobile soft robots.