bound to (be or do something)
Apt or likely to do something. We all thought that Doug was bound to be an artist, so we were very surprised when he became a trader on Wall Street. A: "Do you think it will rain today?" B: "It hasn't rained for weeks, so it's bound to."
bound to do something
certain to do something; destined to do something. Jill's bound to do a good job. We are bound to tell the truth.