Bhakti and Prema Inherent or Foreign ?

Straight forward answer— "Bhakti and Kṛṣṇa Prema are NOT inherent in the Jīva, however it's natural for a jīva to love this search brings them to the real object of Love Kṛṣṇa"

sarvopādhi-vinirmuktaṁ tat-paratvena nirmalam
hṛṣīkeṇa hṛṣīkeśa-sevanaṁ bhaktir ucyate 

“ ‘Bhakti, or devotional service, means engaging all our senses in the service of the Lord, the Supreme Personality of Godhead, the master of all the senses. When the spirit soul renders service unto the Supreme, there are two side effects. One is freed from all material designations, and one’s senses are purified simply by being employed in the service of the Lord.’[Nārada Pañcarātra] 

“sarvopādhi-vinirmuktaṁ”— Freed from all material adjuncts. Nārada Bhakti Sūtra— tat prāpya tad evāvalokayati tad eva śṛṇoti tad eva bhāṣayati tad eva cintayati; “Having obtained pure love of God, one looks only at the Lord, hears only about Him, speaks only of Him, and thinks only of Him.”. Here the ‘prāpya’ is important because it refutes the false doctrine of inherent kṛṣṇa prema in jīva. One may say that if it is so then how does the Jīva have a sthāyī rati ?

The taste for a particular rasa is due to past tendencies or grace of a saint belonging to the same rasa. As Śrīla Viśvanātha cakravarti ṭhākura write in his commentary to Bhakti Rasāmṛta sindhu 2.5.38—

yathottaram asau svāda-viśeṣollāsamayy api |
ratir vāsanayā svādvī bhāsate kāpi kasyacit ||

These five types of rati (from śuddha to priyatā-rati[śānta to mādhūrya]) become progressively more blissful by increasing tastes. The particular taste arises in a devotee according to his previous experiences.

Śrī Viśvānāth comments—

tan-madhye kāpi ratiḥ kasyacid bhaktasya prācīna-vāsanayā svādvī bhāsate | yathā madhurāmla-kaṭv-ādi-rasānāṁ madhye ekasminn eva rase kasyacana prācīna-vāsanayā rucir nānya-rase, tathaiva dāsādy-ekatara-rase kasyacid bhaktasya prācīna-vāsanayā | kiṁ vā, asminn eva janmani tādṛśa-mahat-kṛpayā rucir nānyatreti | kasyacana dāsyādi-dvaye rati-traye ceti sarvatra vivecanīyam ||

Amongst all bhakti-rasas, a particular rasa appears most tasteful to a particular devotee according to his specific vāsanā (devotional tendencies) from previous lives. Just as amongst all food-rasas, namely sweet, sour, bitter etc., a particular rasa appeals to an individual according to his previous vasanā (dietary tendencies), similarly a particular devotee finds one of the bhakti-rasas to be most appealing due to his previous vāsanās(devotional tendencies). It is also possible to develop an affinity towards a particular rasa in this very life by the mercy of a great soul attached to that rasa.

This vāsanā is also developed by the will of the Lord as said in the Bṛhad Bhāgavatāmṛta 2.4.190—
vicitra-līlā-vibhavasya tasya samudra-koṭī-gahanāśayasya
vicitra-tat-tad-ruci-dāna-līlā-vibhūtim uttarkayituṁ prabhuḥ kaḥ
Śrī Kṛṣṇa’s pastimes expand with ever-new variety. His heart is as deep as millions of oceans. By logic no one can understand the purpose for which He has placed different tastes in the hearts of His devotees and expanded the opulence of His pastimes accordingly.

Śrī Nārada continues— mukhyatas tu mahat-kṛpayaiva bhagavat-kṛpā-leśād vā; "Primarily, however, one develops bhakti by the mercy of great souls, or by a small drop of the Lord's mercy." Also because labhyate 'pi tat-kṛpayaiva; “The association of great souls can be attained—but only by the Lord's mercy.” Thus it is proven that vāsanā for sthāyī rati is given by the Lord according to the way he wants to enjoy us.

How does Bhagavān give Bhakti to even those who don't deserve it by default ?, He does that by his Acintya śakti or Aghaṭitaghaṭanāpaṭīyasī śakti. By the previous sūtra we get to know that Bhakti is obtained through sādhu-saṅga, it is not existing in the intrinsic nature of the nitya-baddha because it is bereft of sambandha tattva. Because Śuddha bhakti is eternal [amṛta-svarūpā ca,This pure love for God is eternal.] once achieved it can’t be destroyed. Jīvas are running behind rasa and not Kṛṣṇa, they want ānanda, but Kṛṣṇa is ānanda [anandamaya’bhyasat] and personification of rasa [raso’vai saḥ], so once they reach Kṛṣṇa their search for ānanda is successful As said in the Prīti sandarbha anuccheda 1—

evaṃ tat tvam asi [chā,u, 6.8.7] ity-ādi-śāstram api tat-prema-param eva jñeyam, tvam evāmuka itivat, kiṃ ca, loka-vyavahāroʼpi tat-para eva dṛśyate, sarve hi prāṇinaḥ prīti-tātparyakā eva, tad-artham ātma-vyayāder api darśanāt, kintu yogya-viṣayam alabdhvā, tais tatra tatra sā parivarjyate, ataḥ sarvair eva yogya-tad-viṣayeʼnveṣṭum iṣṭe sati, śrī-bhagavaty eva tasyāḥ paryavasānaṃ syād iti, tad evaṃ bhagavat-prīter eva parama-puruṣārthatve||

Chāndogya Upaniṣad's declaration "tat tvam asi" (Thou art That) actually describes the individual  soul's relation with the Supreme Personality of Godhead is Love [here tat pada is endowed with some relation with the tvam pada with the be-verb asi, are, In simple words- relation of tat and tvam is Love [and also aṁśa, aṁśi bhāva ]]. Love is seen even in the ordinary dealings of the material world. Love is natural for all living beings. It is seen even among the  least spiritual of materialists, among them who have destroyed their spiritual life. How can the soul  give up its nature? Therefore every soul seeks someone to love [being a baby it loves the mother, in toddlerhood it’s friend, in youth their spouse]. That search for love finds its final culmination when one falls in love with the Supreme Personality of Godhead [If someone loves Kṛṣṇa they can’t love anyone else]. Therefore falling in Love with the Supreme Personality of Godhead is the highest goal of life.  

 This is the actual purport of nitya-siddha kṛṣṇa-prema ‘sādhya’ kabhu naya śravaṇādi-śuddha-citte karaye udaya, Love for Kṛṣṇa is natural [because he is the embodiment of rasa which everyone is soughting after], It is not something that is to be gained by austerities, The Love for Kṛṣṇa rises in one’s heart when they come to know that Kṛṣṇa is the source of all happiness and Ānanda that they are seeking, This knowledge of Kṛṣṇa being ‘raso vai saḥ’ and the sole object of Love is gained by faithfully hearing and practicing other limbs of Devotion. Thus this Love for Kṛṣṇa is not something foreign it is intrinsic to the Jīva because to Love is intrinsic to the Jīva and real subject of Love is Kṛṣṇa, Thus by Hearing and svadhyāya one can rise within themselves the Love for Lord Kṛṣṇa.The Nitya svadharma of a jīva is to serve Kṛṣṇa it doesn’t mean that all jīvas serve kṛṣṇa and due to envy towards the lord there comes a lapse in such service, it is not at all like that because it is the nitya svadharma of the jīva, it is a part of the Jīva’s svarūpa lakṣaṇa. Putting in simple worlds, jīvera svarūpa haya kṛṣṇera nityadāsa means Jīva’s svarupa lakṣaṇa [natural charecteristic] is to serve Kṛṣṇa like the 8 other natural charecteristcs but due to beginningless ignorance, such service is not rendered by the Jīva that is why it is svadharmacyuta, fallen from it’s natural duty. Thus the jīva is called Fallen not because it fell from goloka but because it is not doing it’s svadharma, just as a brahmin who doesn’t study the vedas nor teaches the same is fallen from his svadharma of being a brahmin.

All glories to Śrīla Prabhupāda
All glories to Śrīla Jīva gosvāmī 
All glories to Śrī Nārada Muni