You can't bribe the faction leader or the faction heir. And I think that you can't bribe the capital, but I am not sure of this.
Be careful when offering bribes. If you don't have enough money to bribe the army or the city, don't offer it. If the character refuses to be bribed, he becomes publicly loyal and hence that much more difficult to bribe later on. So if in doubt, don't offer a bribe. Hope that helps.