Have you inspected your system, OP, as in getting under the car, making totally sure there are no coolant leaks, removing undertray, running car, making certain nothing is leaking? When I had this problem, it turned out to be a crack in the expansion tank, as I said earlier, that was very hard to find. I saw evidence of dried coolant nearby and after removing the tank I found the crack. I would think bleeding the system, without identifying the problem is pointless.
If you want to test the heater valve, then just bypass it temporarily, see if that fixes your problem. I'm still sticking with leak though. Air in the system will find its way to the heater core.