You can cut glass with a diamond cut off wheel on a dremel. It's not your best option and you need to use water to keep the dust down. You do not want to breathe it.
A better option, less toxic, would be a normal glass cutter. It has been a long time ago, high school, but I think we had an attachment that held the cutter steady, rotate the bottle against the cutter and tap bottle bottom to make the cut.
You are right and this can be the better option to opt so that to avoid glass dust gets into your lungs. Normal glass cutter would be the better option and this will be more helpful but, water is required here too.