Super Glue's 'Original' will dry clear in that use.
You can use clear epoxy.
Many liquid glues dry clear. All cyano-acrylates do.
You can sometimes make it dry faster by heating it,but generally not a good idea as this seems to weaken it also.
Contact glue (impact glue)
Applying heat may release glue. Over time, glue can become so dry that it fails to remain glued.
Elmer's China and Glass glue.
You can use clear epoxy.
let it dry
Elmer's Glass glue would work, but I'd recommend taping the back too.
They do make one that will dry clear. It depends on which you are using. There are a few different types
Use super glue, or a clear epoxy
Many liquid glues dry clear. All cyano-acrylates do.
Epoxy or silicone will both work.
As long as it can cure in dry conditions,
The purple disappears, it just is colored to see where it is on
You can sometimes make it dry faster by heating it,but generally not a good idea as this seems to weaken it also.
To glue glass crystals to wine glasses a clear epoxy resin would be best, or a waterproof cyanoacrylate (most are water soluble so the crystals will come off after several washes).