How long does pulsatile tinnitus last after bells palsy?

Not related. Pulsation tinnitus is not a feature of bells palsy which only refers to facial paralysis or weakness. Pulsatile tinnitus can have many causes. You should have a complete evaluation by an ENT specialist.
They are not related. One doesn't have to do with the other. Pulsatile tinnitus is not a symptom of bells palsy. It is a separate issue.
No association. Bell's palsy is "idiopathic facial paralysis" - meaning no other cause of the paralysis can be identified. It always occurs as an isolated event. If there are other symptoms associated with it... It should be checked. An MRI might be the place to start.