This paper investigates the dynamic stability of bumblebee black holes (BHs) in bumblebee gravity, a vector-tensor theory where a vector field couples nonminimally to the Ricci tensor. The authors focus on the gravitational and vector perturbations of odd parity and find that bumblebee BHs do not suffer from ghost instability. However, gradient and tachyonic instabilities exist when the bumblebee charge exceeds certain values, depending on the nonminimal coupling constant $\xi$. The critical value for the instabilities is $\xi \sim 4\pi G$, where $G$ is the gravitational constant. The stability analysis places stronger constraints on the parameter space of bumblebee BHs compared to recent observations of supermassive BH shadows by the Event Horizon Telescope Collaboration. Specifically, for $\xi(\xi - 16\pi G) > 0$, the charge of a bumblebee BH cannot be larger than its mass, which is reminiscent of Penrose's cosmic censorship conjecture. The paper also discusses the conditions for avoiding both gradient and tachyonic instabilities, providing a no-go theorem on the bumblebee charge.This paper investigates the dynamic stability of bumblebee black holes (BHs) in bumblebee gravity, a vector-tensor theory where a vector field couples nonminimally to the Ricci tensor. The authors focus on the gravitational and vector perturbations of odd parity and find that bumblebee BHs do not suffer from ghost instability. However, gradient and tachyonic instabilities exist when the bumblebee charge exceeds certain values, depending on the nonminimal coupling constant $\xi$. The critical value for the instabilities is $\xi \sim 4\pi G$, where $G$ is the gravitational constant. The stability analysis places stronger constraints on the parameter space of bumblebee BHs compared to recent observations of supermassive BH shadows by the Event Horizon Telescope Collaboration. Specifically, for $\xi(\xi - 16\pi G) > 0$, the charge of a bumblebee BH cannot be larger than its mass, which is reminiscent of Penrose's cosmic censorship conjecture. The paper also discusses the conditions for avoiding both gradient and tachyonic instabilities, providing a no-go theorem on the bumblebee charge.