Like a lot of things in EVE, the Negotiation skill description is not to be taken literally.
Mission rewards are determined by the agents level, location and effective quality.
Effective Quality = Base Quality + (5 * Level of Negotiation) + Effective Agent Standing
Effective quality directly affects the ISK reward, loyalty points earned and your standing gain with the agent and their corporation.
Similarly, the Negotiation skill also affects the amount of research points you get from R&D agents. It may affect other aspects of the game that I am not aware of as well.
As to whether the skill affects both base reward and bonus, I am not entirely sure.