Derive Bode Diagram from difference equation
You can evaluate the frequency response by evaluating $H(z)$ in the unit circle: $H(e^{j\theta})$, where $\theta$ is the discrete-time frequency.

If you prefer a frequency in Hz, then use $\theta = 2\pi/f_s$ (i.e. the sampling frequency corresponds to $\theta = 2\pi$).

The above expression will give you the frequency response as a complex number, signifying both amplitude and phase response.

If you don't have access to complex number algebra on your platform, use either GNU Octave or Matlab to plot the frequency response (using the function freqz, which takes the a and b coefficients you have already).

Note that Bode diagram refers to an asymptotic approximation of the frequency response, valid only in continuous time systems.