The most thoroughly accepted Gauḍīya exact definition of bhakti is from Śrī Rūpa Goswāmī in Śrī Bhakti-rasāmṛta-sindhu 1.1.11
अन्याभिलाषिताशून्यं ज्ञानकर्माद्यनावृतम् ।
अनुकूल्येन कृष्णानुशीलनं भक्तिरुत्तमम् ।।
ānyābhilāṣitā śunyaṁ jñāna-karmādy anāvṛtam
anukūlyena kṛṣṇānu-śīlanaṁ bhaktir-uttamam
“The ultimate bhakti is expression of affection for Krishna, without ulterior motive or occlusion by extraneous elements.”
The extraneous motives and their means of attainment are classified broadly as bhukti (self-centered happiness) pursued by karma (self-centered endeavors), and mukti (freedom) pursued by jñāna (acquisition of objectivity and detachment).
Bhakti has its own intrinsic components of endeavors (anuśīlana) and supra-objective subjectivity (anukūlya) and thus has its own intrinsic happiness and freedom – so there is no need for extraneous endeavor. And the extraneous effort to attain happiness and freedom outside the context of love (bhakti) is a serious flaw that prevents one from actually experiencing true love (uttama-bhakti) at all.