Bail may have been $200k, but one just needs to pay a bail bondsman 10% and the bail bondsman signs you out with the promise you will show up for your court date. If you don't show up, you owe 100% of the bail to the bondsman since he put his name in for you, and thats when Dog the Bounty Hunter gets called. It's standard practice everywhere, thats why the $200K bond was laughable, it should have been a good 2 million instead.
How did he pay only 10% of his bail? He used a bail bondsmen. Normally when you pay bail you get all of it back assuming you show up to court, but since not everyone can make bail, they have the bondsmen who takes a small percentage of the money but doesn't give it back in exchange for paying the full bail. it's a US exclusive thing I believe (they are illegal where I live)
As for why the allegedly rich man is paying the bondsmen and not just the whole bail... well I'll leave that one up to you.
Getting your bail deposit back depends on the state. In my state they keep the 10% and sometimes make you check in weekly until the court date. I reckon if you pay the full bond you could get back all of it minus the bondsman fee for making sure you show.