One "ghost flushing" toilet shouldn't double a water bill. You might have some leaks elsewhere.
Here's a couple of things to try. First, if you have another toilet you can use, shut the water off to the suspect toilet and see if that reduces your water usage. If it doesn't, then you've got issues elsewhere.
Look in the toilet tank. If the water level is very high, you could be spilling water into the overflow tube, bypassing the bowl altogether, which could be the reason for the dye not showing up in the bowl.
If it turns out that the toilet isn't the culprit, you'll have to do more detective work. Here's one way to try and track it down. Shut the water off at the meter and leave it off for a few hours. Now, stand somewhere central in the house and have a friend turn the water back on. Listen very carefully (have any other noise sources turned off -- radios, fans, AC units, etc.). You should be able to hear where the water is rushing to; these are the suspected leakage areas.
--Welmoed the Home Inspector