Yes, there's one zero. I'm not sure how far along you are in your complex math or controls course, but s is the 'generic' frequency [tex]s=\sigma+j\omega[/tex]. If you're finding the frequency response (as you are in a Bode plot) you're only concerned with the situation where [tex]\sigma[/tex] is zero and frequency is imaginary (i.e. sinusoidal). That's why some of the previously-linked resources use [tex]j\omega[/tex] instead of s (even though the transfer function is given in terms of s)
Put another way, if your transfer function is called H(s), you're finding |H(jw)| (the magnitude of the frequency response) and the phase