Bunny had no idea that the fake kidnapping and ransom grift was happening.

Bunny left town on a whim to hang out with other friends. Neither Uli nor the other Jeffrey Lebowski (the millionaire) knew why she had left, where she had gone, or when she might return.

Uli and the nihilists hatched a scheme to pretend that they had kidnapped her so they could demand a ransom from The Big Lebowski.

The Big Lebowski responded to the nihilists' scheme with his own embezzlement plan, which involved a ringer and a deadbeat, someone the square community wouldn't give a shit about. The Big Lebowski may have suspected that Bunny was faking her own kidnapping with the nihilists. Either way, he didn't care. To him, this was an opportunity to keep the ransom, paid by the foundation, for himself.

When the nihilists discovered that The Big Lebowski was trying some funny stuff, they cut off the toe of one of their girlfriends. The Big Lebowski responded by exploiting this turn to further try to convince the Dude that anything that happened to Bunny was his fault.

Bunny returned to the City of Angels like a child wandering into the middle of a movie, even though it was towards the end.

The nihilists were left with nothing, Lebowski, except a toeless girlfriend. Their mistake was in thinking that The Big Lebowski had tried to pay the ransom, that the Dude had stolen the money, and that they could fuck up the Dude, Walter, and Donny to get it back.