I have edited the JailBedScript.psc file which is a script but in order to compile it and add my new properties I need to find it in the creation kit. But I cannot find where it is. Is this script even used in the game? The first line in the script is "Scriptname JailBedScript extends ObjectReference" which means it has to be connected to a Reference of an Object. Any help will be most appreciated!

That script isn't used in the final game. The comment at the top says its author was wanting it to be temporary. It appears they hard coded jail behavior into the game engine instead of relying on that script by the time they released the game. If you've been sent to jail you get the jail special actions no matter where you sleep. I tested with my own portable bedroll mod and it doesn't matter whether I use it or the standard jail bed.

That make sense why when I right click on the JailBedMsg in the Creation Kit under info it wasn't linked to anything. Do you know of a way to detect if the player served his jail time? I know how to detect if a player has gone to jail and escaped by using...

Game.QueryStat("Jail Escapes")

Game.QueryStat("Times Jailed")

But I cannot figure out a way to detect if the person has gone to jail and served their time.

There a game stat for time in prison. You could keep track of that stat this way:

http://www.creationkit.com/index.php?title=OnTrackedStatsEvent_-_Form

Update your stat-tracking after each wait / sleep.

The stat is called "Days Jailed".

I have figure out a way and tested it with every jail in Skyrim and Solstheim. It needs to be in a Quest Script.

Event OnInIt()
	RegisterForUpdate(1.0)
EndEvent

Event OnUpdate()
	If MyJailVar.GetValue() == 0
		If Game.QueryStat("Times Jailed") > MyJailTimes.GetValue()
			MyJailTimes.SetValue(Game.QueryStat("Times Jailed"))
			MyJailVar.SetValue(1)
			MyJailEscapes.SetValue(Game.QueryStat("Jail Escapes"))
		Endif
	ElseIf MyJailVar.GetValue() == 1
		If Game.QueryStat("Jail Escapes") > MyJailEscapes.GetValue()
			;Add Escaped Jail code here
			MyJailVar.SetValue(0)
		Elseif Game.GetPlayer().IsInInterior() == 0
			MyJailVar.SetValue(2)
		Endif
	ElseIf MyJailVar.GetValue() == 2
		If Game.QueryStat("Jail Escapes") > MyJailEscapes.GetValue()
			;Add Escaped Jail code here
			MyJailVar.SetValue(0)
		Elseif Game.GetPlayer().IsInInterior() == 0
			;Add Served Jailtime code here
			MyJailVar.SetValue(0)
		Endif
	EndIf
EndEvent