Question: What is the relation between sādhanā bhakti and citta vṛtti nirodha?
Answer: citta vṛtti nirodha, the cessation of all thought in the mind, as proposed by Patañjali is not a part of sādhanā bhakti. In fact, in sādhanā bhakti, the idea is to create vṛttis related to bhakti.
For example, when chanting the name, one should exclusively try to create vṛttis of the name. All other vṛttis, including vṛttis related to Bhagavān even (such as His form, pastimes etc.), are to be set to zero. The only vṛtti should be the name. When performing other limbs of bhakti- like deity worship, those limbs should be the exclusive focus.
With such exclusive focus on bhakti, bhāva for Bhagavān will manifest eventually, and then Bhagavān will become manifest in the mind internally, or better still, externally to the senses. Sādhanā bhakti gradually deactivates the saṁskāras in the heart which cause vṛttis unrelated to bhakti.
Furthermore, even the citta vṛtti nirodha in Patañjali’s yoga cannot be achieved without bhakti. This is emphatically stated in the Bhāgavatam. Therefore, self-realization which results after citta vṛtti nirodha, and the subsequent Brahman realization is not possible without bhakti (see for example, SB 4.22.39). This is the sequence explained by Śrī Kapiladeva in SB 3.28.34-35:
1. By the means of aṣṭānga yoga meditation on Hari, one develops rati-ābhāsa [semblance of love for Hari]. Next, one withdraws the mind from Hari also, and all citta vṛttis are set to zero. At this point the self-manifests.
2. When the mind then identifies with Brahman, Brahman manifests. This means that both self-realization and Brahman realization occur only because of meditation on Hari.
Question: Is self-realization also necessary for realization of Bhagavān as it is required for realization of Brahman?
Answer: Self-realization is required for Brahman realization because the goal is Brahman, which can only be realized by identification of the pure self with Brahman. As such identification is not the goal on the path of bhakti, self-realization or direct perception of the pure ātman neither precedes Bhagavān realization nor is even a secondary goal on the path of bhakti.