My doctor says to take statin at bedtime because cholesterol is produced more at sleep. does that mean both hdl and ldl are produced at night?

No and no: Please , it seems there's been a misunderstanding. Have your doctor re answer your question. If its the same answer, please see someone else.

Gall bladder: Gall bladder and liver works at night by using fats from heavy meals to convert cholesterol into bile - if there is not sufficient b6, b3, carnitine they cause high cholesterol, ldl(high) and HDL (low) respectively. Fatty meals typically are later part of day - hope this helps.