Have you ever wondered what "is bound to" means?
Let's look at the following sentence:
"With all that practice, you're bound to improve."

So, "bound to" expresses a strong likelihood that the mentioned activity—here, improving—will happen.

In German, we would say something like:
"Mit all dem Üben wirst du mit Sicherheit besser werden."
Another variation would be to use "unweigerlich" or "sehr wahrscheinlich":
"Durch all das Üben wirst du unweigerlich Fortschritte machen."

In English, we could also use the phrase "be likely to," although "bound to" conveys a stronger sense of certainty.
In Japanese we see a similar construction with "に決まっている”.
彼は勝に決まっている。
He's bound to win.
Er wird mit Sicherheit gewinnen.