I am making a turkey in a bag this weekend and I was wondering if there is a sure fire way to know when your turkey is done cooking. I don't have a meat (or any other) thermometer.
Go get a $15 probe thermometer. There is really no point in cooking turkey or any other roast without one.
The actual answer is- there is no good way without measuring the internal temperature. Any time-based approach will be a guess at best.
The built in thermometer in some turkeys is a spring with some epoxy that melts a specific temperature. They are somewhat unreliable and either way they spring at 180F or so. This is well overdone for white meat but covers the turkey seller's liability.
Really- it's worth it to just get the thermometer and take the guess work out.
Use a probe thermometer. A turkey is cooked at 165F (according to the USDA), so you should take it out of the oven around 161F. The turkey internal temperature will keep rising after you take it out of the oven, so cover it with foil, let it sit for 15 minutes after you take it out of the oven and you are good to go.