I am pregnant and my mum had bi-polar. What is the chance my unborn baby will inherit bi-polar?

The known stats. From the literature: 35% chance if one parent has it. 75% if both parents have it. These are the probabilities. Decidedly less in your case, since not parent but grandparent. Keep in mind: more stressful environment will play a major role is pushing these probabilities forward / more stable environment is always protective against gene expression of any genetic vulnerability. Take care.
Studies demonstrate. That bipolar disorder does run in families but the risk is minimal. When 1 parent has this diagnosis, the chances of the child having the illness is between 4 and 15%. When neither of the parents has the illness, the chances are 0 to 2%.