Thanks for the Silicon advice!
I thought I would have to put my light shade project on hold until I could scrounge up enough change to go buy some silicon. As luck would have it, while searching for a light bulb in the tool closet, I happened upon some silicon I bought last year for mounting plant anchors outside on the wall. The silicon worked beautifully. My pebbles stayed put and it was even less messy than working with Weldbond. The only drawback (and this might simply be this particular brand) is that the instructions say to let glass on glass projects cure for a week before doing anything else to the object. So, instant gratification on the one hand, on the other...well, I'm just going to have to be patient! I will post pics once the shade is grouted.