You'll have to wash them one by one.

Can't you spray them with water from a hose? Get them good and wet.

yea, blast them with a hose to flush off dirt - not a pressure washer, they'll end up all over the place...

I live quite near a shingle beach and know that wet pebbles are shiny and dry ones are not. So keep them wet or varnish them.

You might consider choosing another type of material for your border that does not change appearance much when it rains ( take a look at your shiny car after a rain) or gets wind blown with dust and dirt. What you chose looks great for about a week or two but after that......To keep on washing it off will eventually cause your border to sink into a very wet muddy base.

I reckon the only long term effective answer is to replace them with some with shiny coating eg ceramic. Just out of interest, how did you get them shiny in the first place?

They're probably what's sold as 'polished pebbles' they come in sacks from aggregate suppliers or garden centres for landscaping.

The best of those are actually tumble polished, but the majority have been tumbled long enough to make them semi-smooth, and then given a coating with some kind of wax, like car wax. The wax decays over time, and lets the matte surface show through. They can be restored, but it involves taking them up, washing them thoroughly, letting them dry, and tumbling them with wax flakes for an hour or two. Lotsa work!

I know they look nice when shiny but I guess the best thing is pop a few of the glass ones amongst them, otherwise it sounds like a lot of hassle, you really do not want to end up with a soggy mess...