Women with Bipolar Disorder have at least a 1 in 4 risk of suffering a severe recurrence following delivery.
Source- Di Florio A, Smith S, Jones I. Postpartum psychosis. The Obstetrician & Gynaecologist 2013;15:145–50.

Bipolar women with a personal or family history of PP are at particularly high risk with greater than 1 in 2 deliveries affected by PP.
If it is only a personal history of Bipolar disorder ( Not Postpartum Psychosis ) then the risk is 1 in 4.
Source- The Obstetrician & Gynaecologist 2013;15:145–50.