Anonymous
The bonus will return $900 as you said, so you want to bet an equivalent amount on the 1.09 side to return $900 as well. This amount is $825.68 (you’d just bet the $825 though, not an abnormal amount including the cents). So either way you’re $900, and you’ve outlaid $825.68, so you’ve made $74.32 profit ($900-$825.68).
So with the aid of the $100 bonus, you’re making $74.32 profit, so you’re returning 74.32% of the bonus.