The term "permanent" in reference to ink may make you think that a stain from a permanent marker can never be removed. Luckily, this isn't always the case. If you have a permanent ink mark on a glass bottle or other similarly smooth surface, you can usually remove the stain quite easily. You don't even have to spend money on expensive cleaning products. Contrary to what common sense might dictate, you actually create a bigger stain to get rid of the first one.
Color over the permanent marker stain with a dry erase marker. Be sure to cover the entire stained area.
Wipe off both the dry erase and permanent marker marks with a paper towel. When you remove the dry erase marker, the permanent marker will come off with it.
Spray some glass cleaner or white vinegar onto a paper towel and use it to clean the glass bottle and remove any lingering ink residue.