Vesper's initial mission from the organization (later found out to be Quantum) was not to steal the money, but to sabotage Bond.
The Organization 'kidnapped' Vesper's boyfriend in order to blackmail her in exchange for his life, for which her mission was to ruin Bond's chances of winning.
This is because Quantum want Le Chiffre to win. They were the ones who risked their reputation with the African warlord at the beginning of the movie to recommend Le Chiffre to be their investor.
Le Chiffre puts on the poker game in order to win their money back, not Quantum's. So they plant Vesper in order to make sure Bond doesn't win, which is why it is she who tells Le Chiffre that Bond has discovered his tell, and not Matthis as Bond later suspected, and this causes him to lose all of his money, and takes him out of the game as Vesper will not give him any further money.
Had things gone to plan and Felix and the CIA not intervened, Le Chiffre would likely have won. However when he loses he kidnaps Vesper and tortures Bond in order to get the $115 million.
When Mr. White from Quantum intervenes in the torture, it is explained by M near the end of the film that Vesper made a further deal at that time. If Mr. White spared Bond, she would retrieve the password for the account from him and then steal the money.
This was obviously a lot more risky than simply hindering Bond's chances of winning, hence why the initial plan was simply for Le Chiffre to win and keep the money, allowing him to pay back the warlord.
