I would love to know how to attach herb "buckets" to a fence?

You can buy zipper ties to secure them. They come in all colors so they can be hidden in plain sight as a security measure.

Nails or Hooks.........

Could you possibly drill 2 holes in the back side of the "buckets" and screw the buckets to the fence? Hope that helps. :)

See if these links help!

https://www.amazon.com/slp/fence-planters/ov33u3fec93d6hc

https://www.homedepot.com/b/Outdoors-Garden-Center-Pots-Planters-Vertical-Wall-Planters/N-5yc1vZc8so

https://www.backyardboss.net/28-super-unique-and-easy-to-make-fence-planters/

depending on what the buckets look like, there are fence mount brackets available

I bought window boxes at Aldies that were reasonable and adjustment screws on them for varying widths where you hang them. We put them on top of a privacy fence and between the adjustment screws and the weight of the boxes with soil and plants we never had a problem with them getting blown around and we sometimes get storms with some pretty good winds and they never moved. Perhaps you could use something like that and put a couple of herbs in each. We used ours with yellow and red tuberous begonias and they grew great with three in each and they grew into large plants.