Even if you have nothing to do the whole day, she does not need to know that. It's imperative to give the impression of having a busy and eventful life. Of course, it's even better if you actually have one. Also, it's best to call in the middle of the week if you're going to ask her out for the weekend.
This will allow sufficient time to prepare for the possible rendezvous. After leaving a message, all that's left is to wait for a return call. Days later, could it be possible that she's not calling back? No, that's not possible. The message must have gone astray, right? Well, if the message was left to somebody else, there's a relatively good chance that she didn't receive it. So feel free to call back after a day. If it's left to some sort of answering service, chances are she received it and just doesn't want to call back.
If she leaves a message, you might want to wait a day to call back so as not to seem to be at her every beck and call. Exceptions apply when the message goes somewhere along the lines of, "Help, my house is on fire! Just make sure that the calls you make are meaningful. You might even send a personalized gift or card just to remind her of you. Generally you can't call your girlfriend too often unless of course she's finding reasons to cut the conversation short. This is a sign that she is showing traces of suffocation.
Three times a day just to say howdy is a bit much. As is with the other important things in life, when it comes to calling your girlfriend, it is the quality and not the quantity that matters most. And above all, don't forget to call when you say you will.