If one child in a family has bipolar disorder, how likely is it that another child will get it too?

Higher risk. A study in the lancet (2009) showed that if sibling a has bipolar, the sibling b is 8 times more likely to develop bipolar disorder. Other studies place the relative risk range between 7 and 10 times. This translates to a 5-20% risk.
Small. Small but greater than chance. Although there are genetic predispositions in the development of bipolar disorder it clearly is not the significant determiner.