Hi Pete,

Welcome to the forum & good luck to you.

What happened to me is that because I also had already a car driving licence I had to cancel my licence and request a new one for car and motorbikes.

THe first impression reading your post is that you came across some incompetent police man who thought to go rought on you. If Chinese people can have a motorbike driving licence in Tianjin then you also can.

I don't understand why Tianjin should not issue motorbike licences all together, I live in Hangzhou ( a dry city) and I could obtain a driving licence here....

I would suggest first to verify if is possible for a Chinese national to obtain a motorbike driving licence, if yes, then go to the MAIN traffic management police station and ask there.

Normally speaking you need to cancel your current driving licence, apply for a new one for motorbike & car, wait a while, do a written exam and that's it.
Take care the process is time consuming and you could face from couple of weeks to more than a months without driving licence.