I got a bamboo brand stylus today and this thing works well on an iPad screen that doesn't have a screen protector on it.
Why do I mention the no screen protector covered screen? I took off the screen protector, and my original no name stylus that I was using, gripped the glass screen and made writing difficult.
I will update you on the condition of this bamboo brand stylus after using it for a while.
My vision is that it lasts a long time.