You may need specialty glass. Much of the soft or soda-lime glass contains an iron impurity, giving it a greenish cast (i.e. plate glass, window glass.) In general, a trace of other minerals are added to "redden" the green so the human eye can't discern it. If you're going to do fluorescence with glass, you will have to tell your supplier so, so they can sell you glass formulated appropriately, but it may be expensive.
When I was working with laser fluorescence, in the visible using lasers, we had two types of glass: straight up, cheep, window glass, used basically for sizing and identifying the shape of things that would go into the device. It had a noticeable green color, when viewed from the side of the sheet. For actual use under the laser, we used Tempax(tm), a grade of Pyrex glass, it was clear when viewed from the side. But you will find that difficult to melt in an art furnace.