Note also that "I'd like to speak to her directly" does not necessarily mean "I'd like to speak with her right now." In fact, the more common meaning of "to speak to her directly" is that "I'd like to speak to her in person, without going through another person." For example, if you are a customer unhappy with the service you received, and the sales clerk says to you "I will take this matter to my supervisor," you can say "No, I'd rather speak to him (her) directly."

They both mean basically the same thing. You want to speak with her at once, without any delay. However, "right now" is the more commonly used of the two.