Can bell's palsy affect both sides of the face?

Rarely. Bells palsy his weakness of the facial muscles perhaps due to a viral infection in the facial nerve. It is rare for this to affect both sides of the face. Anyone who presents with new facial weakness should be thoroughly evaluated by either a facial surgeon or a neurologist.
Very Unusual. Bell's palsy is idiopathic (no known cause) facial paralysis. It is highly unlikely to affect both sides of the face.. Either at the same time or delayed.