My 80-year-old mother is incontinent and dribbles on chairs while we are in public. How can I approach the subject of wearing a protective pad?

I was surprised that a top request from "anysoldier.com" from female soldiers was pantiliners. So if she can understand, tell her that these days, all women (even soldiers) wear thin pantiliners to protect their underwear and cloths. And for just dribbles, these pads are very very thin. Perhaps the word "pad" is a trigger.

Have some in your purse, and offer her one of YOURS. ;-) Then, "hey, let's buy you a box."

I think the direct approach is called for. Tell her that you noticed that she has been having issues with bladder control and that there are many products that can help her be both mobile and protected.
My Mom uses Poise and Tena...they work very well.
Also, if she could get in the habit of going to the bathroom to void every 2hrs. or so, it will prevent accidents; and I also heard that it helps strengthen the bladder muscles.