Do points on my licence from car offences count against me on bikes, and the other way round?
They do. Once you reach 12 points, you are looking at a minimum 6 month ban, unless you can convince the magistrates that there are mitigating circumstances which mean you deserve mercy. Losing your job is not a reason for avoiding a ban by the way. Being a celebrity, or member of the royal family, may be helpful however, depending on your charity commitments.