'be bound for' is correct and usable in written English.
You can use it to mean to be destined for or heading towards a particular destination. For example, "The train was bound for Madrid".
Conroy is understood to be bound for a corporate job.
All four would be bound for the west coast, to ensure maximum fuel- load.
Its carcass would be bound for burning rather than the family freezer.
If he can repeat those numbers, this team could be bound for the postseason.
Unlike Hamels, he could be bound for the majors without more waiting.
King Charles III is surely – it should be – bound for the West End.
When the Rangers return home on Sunday, the young goalie will be bound for the minors.
Villanova's national championship football program could be bound for the Big East.
With about 200 other men he was put on a vessel supposed to be bound for Alexandria, Va.
Phil Bardsley, recently pictured lying in a bed of £50 notes in a casino, could be bound for Hull.
If it gets its way, the whaling fleet could be bound for the Antarctic by the end of next year.
