How do you explain to your child that you are bipolar?

Depends. It depends on your childs age and level of maturity, preschoolers and school age children are going to have a hard time understanding the concept...From mommy is sick to sometimes mommy feels very happy and other times very sad could be enough. Middle schoolers and up, downloading patient information from a medical site or asking your md to explainit to the child could be viable options.
Your? Shows your love. Do your meds allow you to parent the way you'd like (discipline consistently, use time-out effectively, read & play, & praise good behaviors), or are you concerned that you might do something you'll regret.? With only 1 parent with bpd, your child's risk is 20%. Does (s)he have behavior/learning problems? Don't worry or feel guilty; contact nami & your pede to get into a child psychologist.