Analogread causing servo to misbehave

Servo servo1;

This does not even begin to hint at what the servo is doing. A more meaningful name would not be a waste.

  servo1.attach(6);

Which is a PWM pin. Does attaching the servo to another, non-PWM, pin make any difference?

  digitalWrite(14 + DoorBellPin, HIGH);		// set pullup on the analog pin

But, you are not using the analog pin as a digital pin, so why are you doing this?

  if (DoorBellPinVal < 100) {
    if (currentMillis-DoorBellValTriggeredMillis > debounce)  	// And if we're not within debounce time
    {
      DoorBellTriggered = 1;
	  DoorBellValTriggeredMillis = currentMillis;
	}
  }

And, if DoorBellPinVal is > 100, what happens? If the interval is less than debounce, what happens?

When I'm writing code, if(something) is immediately followed by {, }, else, {, and } follow immediately. Then, I determine what code belongs in each block. Having the empty else block stare at me ensures that I don't forget to deal with the not true condition.

Sometimes that simply means deleting the else block, but its presence serves to remind me that I need to consider the case.

The else block to move the servo back is attached to the if(Button1State) statement. Again, I'd like to encourage you to use more meaningful names. I don't see where Button1State is assigned a value before it is used, nor do I know what it means. So, I can't tell if the else statement is in the right place, or not.

The mix of styles, with some { on new lines and some on the line with the if statement, and the random indentation do not help with seeing the structure of the program. Pick one style (I prefer the new line style myself) and stick with it. Use Tools + Auto format again (and again and again, if necessary as you revise the code.