"is bound" is correct and usable in written English.
You can use it to describe an inevitable situation that is likely to take place. For example, "He is bound to succeed in life with so much determination and hard work".
Dictionary
is bound
verb
Past of bind
Exact(60)
THE performer is bound.
She is bound.
Something is bound to happen.
It is bound to retaliate.
It is bound to fail.
Conflict is bound to ensue.
There is bound to be skepticism.
And it is bound to last.
This is bound to make things worse.
This is bound to reshape police priorities.
That is bound to arouse suspicions.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com