The Lord appears by His independent will as Kṛṣṇa in the Yadu-dynasty and as Rāma in the Raghu dynasty. So too does He appear in the external and internal senses of His devotee.
Like the Lord, His self-manifesting internal potency Bhakti-devī is eternal and by her own independent sweet will, she appears to the internal and external senses of the devotee. Her appearance does not depend on any cause.

From the description in Gopāla Uttara-tāpanī Upaniṣad it can be clearly understood that Bhakti-devī is also eternal like Kṛṣṇa and is full of knowledge and bliss. vijñāna-ghana ānanda-ghana sac-cid-ānandaika rase bhakti-yoge tiṣṭhati: “Śrī Kṛṣṇa, the personification of absolute knowledge and condensed  bliss can be attained by the mercy of sac-cid-ānanda-mayī bhakti.”

This text gives the description of the svarūpa (form) of the Supreme Lord and the svarūpa of bhakti that makes him subdued by His devotees. If bhakti were not sac-cid-ānanda-mayī, it could never make the Lord subdued by His devotees. Bhakti is cid-ānanda-mayī, self-manifesting and completely beyond the material nature.

One may ask, how then can it manifest in the material senses of a devotee? The answer is that an iron bar put into burning fire attains the same quality as fire, so too bhakti, by its own potency, destroys the material nature of the senses of a devotee, transforming it into spiritual nature like her own. Finally she manifests herself in the spiritual senses of a devotee.

Śrīmat Jīva Gosvāmī specifically describes the svarūpa of bhakti in Prīti-sandarbha (65) –
bhaktir evainaṁ nayati bhaktir evainaṁ darśayati bhaktivaśaḥ puruṣo bhaktir eva bhūyasī iti śruyate. tasmād evaṁ vivicyate. yā caivaṁ bhagavantaṁ svānandena mādayati sā kiṁ lakṣaṇā syāt iti na tāvat sāṅkhyānām iva prākṛta sattvamaya māyika ānanda-rūpā bhagavato māyānabhibhāvyatva śruteḥ svatas tṛptatvācca. na ca nirviśeṣa-vādinām iva bhagavat svarūpānandarūpā atiśayānupapatteḥ. ato natarāṁ jīvasya svarūpānanda-rūpā atyanta kṣudratvāt tasya. tato hlādinī sandhinī samvit tvayyekā sarva saṁsthitau. hlādatāpakarī miśrā tvayi no guṇa varjjite. iti viṣṇu purāṇānusāreṇa hlādinyākhya tadīya svarūpa śaktyānanda rūpaivetyavaśiṣyate – yayā khalu bhagavān svarūpānanda viśeṣībhavati yayaiva taṁ tam ānandam anyānapyanubhāvayatīti. atha tasyā api bhagavati sadaiva vartamāna tayātiśayānupapattes tvevaṁ vivecanīyaṁ śrutārthānyathānupapattyarthāpatti pramāṇa siddhatvāt. tasyā hlādinyā eva kāpi sarvānandātiśāyinī vṛttir nityaṁ bhaktavṛndeṣveva nikṣipyamāṇā bhagavat prītyākhyayā vartate. atas tadanubhavena śrī bhagavān api bhakteṣu prītyatiśayaṁ bhajata iti-

“Śrutis say bhakti brings one near to the Lord, bhakti makes one see the Lord, bhakti brings the Lord under her control, bhakti is the supreme path for attaining the Lord.” The point to be considered here is, what is the specific quality of bhakti that overwhelms even the Lord with bliss? One cannot consider bhakti to have material nature and material bliss as the sāṅkhya philosophers do. According to the śrutis, the self-satisfied Lord cannot be attracted by any material object nor can one consider bhakti as the svarūpānanda, or the bliss existing in the eternal form of the Lord, as accepted by the non-personalists. The Lord enjoys the bliss derived from bhakti (bhaktyānanda) more than the bliss arising from his own svarūpa (svarūpānanda). Nor can one consider bhakti as the bliss existing in the eternal form of the jīva since the bliss of jīvānanda is extremely minute and is thus unable to overwhelm the Lord. The Viṣṇu Purāṇa (1.12.69) says, “The three eternal energies, namely, hlādinī, sandhinī and samvit exist in the svarūpa of Bhagavān, the possessor of all energies. O Lord! Being completely free from the three modes of nature, the material modes, namely, happiness (sattvikī), misery (tāmasi), and the mixture of both (rajasi) do not exist in Your svarūpa.” This text clearly suggests that bhakti is neither svarūpānanda nor jīvānanda. Thus, the only bliss that  remains is that arising from the hlādinī-śakti of the Lord (svarūpa-śaktyānanda). It is this hlādinī-śakti only that overwhelms the Lord with ecstasy. By this śakti the Lord Himself attains bliss and bestows bliss on his devotees.”

One may argue that since the svarūpa-śakti always exists within the svarūpa of the Lord Himself, then how can the Lord be overwhelmed by His own śakti? To clear this doubt one can take the help of arthāpatti evidence, inference from the circumstances. A phenomenon appearing contradictory, though its effects are being observed, can only be proven by arthāpatti. Although it is impossible for hlādinī to give more bliss to the Lord than the bliss existing in His own form, still He is getting more bliss from her. This contradiction can be solved by arthāpatti. For instance, a man named Devadatta does not eat during daytime but still he is fat. According to arthāpatti one has to accept that he may eat during the night. Similarly, by arthāpatti one must accept that no one can give bliss to the Lord other than the hlādinī-śakti, but still He gets bliss that He cannot get from her. According to arthāpatti pramāṇa she is giving Him bliss in another form, just as must be assumed that Devadatta is eating at night. The supremely blissful state of hlādinī that eternally exists in the devotees is known as bhagavat-prīti, or divine prema. The Lord can also experience this within His devotees and thus the Lord and His devotees become attached to each other.

Bhakti is called the svarūpa-śakti of the Lord. The Lord’s svarūpa is sat cit ānanda, so His cit-śakti has also three features, sandhinī, samvit, and hlādinī. Sandhinī is the energy related to existence. By this energy the Lord maintains His own existence and that of others. Samvit is the energy related to knowledge. Through this energy the Lord knows about Himself and causes others to know Him. Hlādinī is the energy related to bliss. By this energy the Lord Himself experiences bliss and gives bliss to others.

Existing within the svarūpa of the Lord, eternity (sat), knowledge (cit), and bliss (ānanda) cannot be separated from each other. Sandhinī, samvit, and hlādinī are similarly inseparable. In any manifestation of svarūpa-śakti, one of these three states is predominant while the other two are also present in lesser quantity. As cit-śakti is self-manifested, its three states are also self-manifesting. They make their appearance by themselves and cause the appearance of others. By the specific self-manifesting state of cit-śakti consisting of hlādinī, sandhinī, and samvit, the Lord appears in His original eternal form along with His associates and transcendental abode. This specific state of svarūpa-śakti is known as viśuddha-sattva. When sandhinī-śakti predominates in viśuddha-sattva it is known as ādhāra-śakti, the energy holding all existence. The abode of the Lord and the Lord’s associates appear by this energy. When samvit-śakti predominates, it is known as ātmavidyā, spiritual knowledge. When hlādinī predominates, it is known as guhya-vidyā, secret knowledge. By this energy bhakti, or bhagavat-prīti, love for the Lord, is manifest.

One can thus understand from this description that bhakti is self-manifesting by nature just like the Lord. There is no other cause for her appearance. Bhakti manifests herself in the devotee by her own independent will. sādhana bhajana is performed to make the heart suitable for her appearance.
(Śrī Rādhākuṇḍa Mahānta Paṇḍita Śrī Ananta Dās Bābājī Mahārāja , tika to Mādhurya Kādambinī)

Translated by Sri Advaita dasji