The shower surround is attached to studs but where the heavy glass enclosure should attach there are no studs. Is there some kind of anchor I can use to attach to the plastic only?
Glass shower enclosures are typically supported by the walls and specifically studs in the walls. Often they will be attached through the shower surface (tile, granite, etc.) if it's structurally sound. Glass is heavy. The biggest issue is typically with the door because it is hinged (suspended) on one side. Some of the weight of the door can be offset with metal framing around the glass enclosure and the door. However, the door must be fastened into a supporting wall stud and preferably a double stud.
The short answer here is No! You don't want to try to mount glass directly to a plastic shower enclosure. You need to get a professional involved here if you haven't worked with this before. If it's not mounted properly it can be dangerous.