In mouseMoved(), set a start time. In draw(), check if time difference between current time and last mouse move time is above 3s. If so, move your bar.

Well there's always the Reference...

Here's one crude approach, working on the assumption that most of the time the mouse will be in motion and that counter>90 is more or less equivalent to 3 seconds at FrameRate(30):

Code:

int counter = 0;

void setup() {
frameRate(30);

}

void draw() {
  counter ++;
  if (counter> 90) {
    // hide stuff;  
    println("hide me!" + counter);  
  }
}

void mouseMoved() {
  counter = 0;
} 

Mind you it's worth mentioning that your interface concept is a little odd...  It's not entirely intuitive to click on something that isn't there in order to make it appear.  Perhaps better to fade it in as the mouse position approaches it; and in fact fade it out as the mouse position leaves it.  That would strike me as more consistent at least...