Rather than bake the mug for 30 minutes I left it for a full hour.
In the end, it looked great...except my writing sucks. I hand washed it and the ink stayed put. I ran it through the dishwasher and I am happy to report that the ink remained.
It has been about 3 weeks since I did this little project and the ink has started to fade and come off.
I read somewhere that Sharpies come in an oil base. I haven't bothered to look but if they do I would think that would be more permanent.