Bump castor is a measure of castor angle change with wheel travel. It is expressed in degrees of castor change per metre of wheel travel. Bump castor occurs due to the fact that the wheel swivals about a castor pole during its travel as shown below. Using a double wishbone suspension as an example, a simplified representation of the the castor pole in side-view is the intersection point of a plane going through the upper control arm and the lower control arm.
As discussed in the post on castor angle and castor trail, suspension trail is a combination of castor trail and pneumatic trail. Suspension trail is a major contributor to the steering feel of a car. A reduction in pneumatic trail as the tyre reaches its limit of grip can be felt by the driver as a change in steering wheel torque. Any unwanted change in castor trail due to bump castor would have the same effect and would give false feedback to the driver.
Bump castor should not exceed 20-30 Deg/m on a front suspension to minimise the effects discussed above. On a rear suspension, higher values are acceptable. Values between 30-90 Deg/m would be typical as this gives greater freedom to improve the anti-lift and anti-squat performance of the suspension. It also can allow greater levels of kinematic wheel centre recession to improve ride performance.