Chapter 12 of Bhagvad gita is named "Bhakti yoga" . It describes path of completely loving devotion to God in very detailed manner. Bhagvad gita is among Prasthantrayi scriptures of Vedanta Philosophy. So that obviously means Bhakti yoga is atleast as old as Gita or even far more older. that definitely pushes it hundreds/thousands years before Christ
see :
- https://www.esamskriti.com/e/Spirituality/Bhagavad-Gita/Bhagavad-Gita~Chapter-12-Bhakti-Yogah~Yoga-Of-Devotion-1.aspx
- http://www.bhagavad-gita.org/Gita/chapter-12.html
Now, This book "Bhakti yoga for beginners" ; shows that bhakti yoga is dealt by Sama veda.
Regarding bhakti "movement", the link which you refer only talks of "movements" in context of modern day or middle era; and that too as per western interpretation. But In ancient era, narad, hanumana(post-ramayana war) were themselves bhakts roaming and chanting around everywhere. These examples and also Panchratra agama indicates powerful presence of bhakti "movement" existing before Buddhist era.