The term 'bid ADIEU' is a phrase used to express a formal FAREWELL. It is derived from the French phrase 'ADIEU, ' which means 'FAREWELL.' The crossword solutions for this term are 'PART, ' 'LEAVE, ' 'AROSE, ' 'ARISE, ' and 'DEPART.' Each of these words can be used to describe the act of saying goodbye, either literally or figuratively. For example, 'PART' can refer to the physical separation of two people, while 'LEAVE' can refer to the emotional separation that occurs when someone departs. Similarly, 'AROSE' and 'ARISE' both refer to the act of rising up, which can be interpreted as a metaphor for leaving a place. Finally, 'DEPART' is a more direct way of expressing the idea of saying goodbye.