Cash won't smooth your way through the requirements, attempting a bribe will probably get you deported.
The bond, refundable, is to guarantee that French Polynesia won't have to pay to send you back to your country when it's time for you to leave. *If you are an American citizen, you need not obtain a visa until you arrive, but to stay longer than 90 days you will have to file for an extension and pay the going fee. *If I remember correctly, this must be done in Papeete.
You can check out of French Polynesia from many of the islands, but must give several days (perhaps up to a week) notice to the officials and bank on the island from which you plan to leave so they can arrange for the money to be there.
The French have elevated bureacracy to an art, and smiling and going along with them is the only way to survive. *If you annoy the postal employees you won't get your mail. *If you tick off the customs and immigration people you won't get to stay. *
We loved French Polynesia, and regretted that we didn't try to find a way to stay, or come back, for a second season. *Back then, though, we still thought that we should be making reasonably efficient time. *How foolish we were! *And how much more fun it was to dawdle so much in so many places!