The glass on your stove is very durable, it is made from a kind of quartz. There is only one glass manufacturer (Schott) that makes the glass for all the glass top stoves in North America and Europe. Bella Copper Diffusers will not hurt the glass, the copper heat diffuser is just like a flat copper pan.
1. As with all stove types use low to medium heat, medium high at the highest and start slow, the copper takes time to heat up.
2. Do not leave the copper diffuser by itself (with no pot with food in it, or with just an empty pot alone with the burner on. It will get too hot and if left for too long may damage the glass. (There is supposed to be a safety sensor on your stove to prevent damage - but you don't want very hot things on your stove anyway.)
3. The copper will get hotter than a regular pot and may cook on a white residue on the glass top stove. This is normal for regular pots, too, but for new stoves may be a surprise for the owner. The residue is not from the copper but is food residue (sometimes invisible residue) which is already on the stove, and may just be lime from your tap water. It can be removed, but it is difficult - the glass manufacturer says that you may need to get "very aggressive" including using a razor blade scraper.
See your stove owner’s manual, or see the glass manufacturer site (Schott glass) for cleaning tips here.
4. The glass manufacturer recommends not sliding any copper and aluminum cookware on the glass - this is because the glass is harder than the metals and the metals will scrape off on the glass - this mark is very hard to remove. Just use caution and don't slide it around.
5. As with all stoves, the copper will discolor with the first use--this is normal.