1
general::
see BOUND TO., Be certain or destined to; also, be determined or resolved to. For example, We are bound to hear from them soon, or No matter what they say, she is bound to run for mayor. This usage is derived from the older sense of bound as "obliged." [Mid-1500s]
American Heritage Idioms
2
general::
Phrase(s): 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.
McGrawhill's American Idioms And Phrasal Verbs