No, their character arc isn't concluded.
The end of The Shadow Rising doesn't really do anything conclusive with the characters of Bain and Chiad; they're still with Perrin and Faile in the Two Rivers, and we just need to wait for that plotline to start moving again.
As it happens, you'll have quite a long wait, because this is one of those times in the series when one of the most major characters completely disappears for the length of a book and their plotline is only picked up again in the next book. So you won't be seeing Perrin, Faile, Bain, or Chiad throughout The Fires of Heaven, and we only return to the Two Rivers at the start of Lord of Chaos, when
Perrin decides that he needs to go to Rand. Later on in the book, Bain and Chiad are with Perrin and Faile when they arrive in Caemlyn to see Rand.
In A Crown of Swords and The Path of Daggers, they
also accompany Perrin and Faile to Ghealdan, and they're with Faile when she's kidnapped by the Shaido and taken as gai'shain.
So as you can see, they're still going to be cropping up in the story for quite a while yet. However, they're never again quite such major characters as they were in certain parts of The Shadow Rising.