The answer is you simply don't get your money back from a casino. Once you lost it playing one of many of their games, you aren't recovering it. You can get comps but that's all. I know this isn't what you wanted to hear, but it is the truth.
To cash out your casino bonus, you will typically need to complete certain requirements set by the casino, such as fulfilling the wagering or playthrough requirements. These requirements usually require you to wager a certain multiple of the bonus amount before you can withdraw it.