How long does it take high BP to cause a stroke?

Many years. For high BP to cause vascular disease of the head and neck vessels. If high enough can have immediate bleed - hemorrhagic stroke. Keep BP under control. See stroke.Org for risk factors.
Variable. There are many types of strokes. Hemorrhage may occur any time in uncontrolled hypertension. High BP causes narrowing of blood vessel and damage to the lining of arteries that inturn can cause stroke. This process takes some time to develop years sometime. There are many other factors working too.