Is 'to be bound to" the same as "be going to"?
I'm going to start writing the article.
I'm bound to start writing the article.

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the second one means you have to do whether you are willing or

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No, it isn't: https://idioms.thefreedictionary.com/be+bound+to

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The second example is unnatural.

That was bound to happen.  (It was predictable or inevitable given the circumstances)

Tom got a speeding ticket.
It was bound to happen. He always drives over the speed limit.

She’s bound to get fired. She’s completely unreliable as an employee.