I also have Corel Draw X5 on one of my Windows machines. Using Corel Draw, I was able to curve a straight line to follow the surface of the mug. Then, I was able to type on the curve, and once the text was on the curve, Corel Draw offered a drop-down selector below the top menus with several options to effect how the text sits along the path.
When you hover over the drop-down in Corel, the tooltip states "specify how the text bends to follow the path".
The third option in this drop-down makes the text appear like it was painted on the surface of the mug. (achieved in a matter of seconds)
Does Adobe Illustrator offer anything like this?