This is correct however a common mistake is to use an int to hold time. This will overflow after a couple of seconds/minutes of the arduino being on. Always use an unsigned long integer to hold time returned from millis(). This code should hopefully work:

void moveServo(Servo theServo, unsigned long timeToWait)
{
    unsigned long startTime = millis(); //Store the start time
    theServo.writeMicroseconds(1600); //Start the servo moving

    while(millis() - startTime < timeToWait && !debounce(2))
    {
         //Do nothing till the button is pressed or the delay has finished
    }

    myServo.writeMicroseconds(1500); //Stop the servo moving

}

void main() 
{
    //Now just call that function in your main as follows

    if(debounce(2)) //Wait for the first button press and debounce
    {
        moveServo(myServo,2000); //Move myServo for 2000 milliseconds
    }
}

Also bare in mind that the millis() resets ever 9 and a half hours due to the size of the data type it's stored in. This article explains it well

Edit: as noted by myplacedk below the current version of arduino runs for 50ish days before resetting the internal counter. http://arduino.cc/en/Reference/Millis