Does rose water ever expire?

Yes, anything with water will expire. If it contains a preservative or was made with distiller water, then it may last about 6 months. If it was made with tap water and no preservative, it's only good a few weeks and that's if you keep it refrigerated. I owns business that makes natural health and beauty products and I've made a lot of floral waters, so I have first hand experience when testing products and have seen some nasty things develop in water if its not preserved or made correctly.

I'm not sure that it will never expire, but bacteria need three things to grow: Water, the right temperature, air.

If the bottle is still sealed (even though that is technically not air tight), then rose water should last for a fairly long time actually.

But once it's opened, it is to be treated with caution after a few weeks.

This matter is especially tricky because, to my knowledge, most of those rose water bottles that come from countries that have less than strict health & safety controls, and not all the bottles have expiry dates.