不知 is more literary and polite than
不知道. Using
不知 at the start of a question softens it —
不知您是否有空?(I wonder if you're free?) sounds much more polite than
你有空吗?. The expression
不知不觉 (bùzhī-bùjué, 'without knowing, without feeling') meaning 'unknowingly/before you realize it' is extremely common.