Brajsunder Das: Some of our Acharyas say that Sukadeva Goswami heard Srimad Bhagavtam from Lord Shiva when He was reciting Srimad Bhagavtam to Goddess Parvati. In Srimad Bhagvatam 2.1.8, Sri Sukadeva Goswami confirms that he also heard it from his Father Srila Veda Vyas.

idaḿ bhāgavataḿ nāma

purāṇaḿ brahma-sammitam

adhītavān dvāparādau

pitur dvaipāyanād aham

Translation: At the end of the Dvāpara-yuga, I studied this great supplement of Vedic literature named Śrīmad-Bhāgavatam, which is equal to all the Vedas, from my father, Śrīla Dvaipāyana Vyāsadeva.

Further, In 1.2.2 of Srimad Bhagavatam, Suta Goswami says:

sūta uvāca

yaḿ pravrajantam anupetam apeta-kṛtyaḿ

dvaipāyano viraha-kātara ājuhāva

putreti tan-mayatayā taravo 'bhinedus

taḿ sarva-bhūta-hṛdayaḿ munim ānato 'smi

Bhagvatam 

Translation: Śrīla Sūta Gosvāmī said: Let me offer my respectful obeisances unto that great sage [Śukadeva Gosvāmī] who can enter the hearts of all. When he went away to take up the renounced order of life [sannyāsa], leaving home without undergoing reformation by the sacred thread or the ceremonies observed by the higher castes, his father, Vyāsadeva, fearing separation from him, cried out, "O my son!" Indeed, only the trees, which were absorbed in the same feelings of separation, echoed in response to the begrieved father.

So how Did Sukadev Goswami come back to hear Srimad Bhagavatam from His father when he left for forest. Srila Sukadeva Goswami replies in SB 2.1.9

pariniṣṭhito 'pi nairguṇya

uttama-śloka-līlayā

gṛhīta-cetā rājarṣe

ākhyānaḿ yad adhītavān

TRANSLATION:  O saintly King, I was certainly situated perfectly in transcendence, yet I was still attracted by the delineation of the pastimes of the Lord, who is described by enlightened verses.

When Srila Vedavyas saw he was not able to bring back his son. He send his disciples asking them to recite two slokas from Srimad Bhagavatam which He compiled after Narada Muni's instructions.

The two slokas are 

SB 3.2.23

aho bakī yaḿ stana-kāla-kūṭaḿ

jighāḿsayāpāyayad apy asādhvī

lebhe gatiḿ dhātry-ucitāḿ tato 'nyaḿ

kaḿ vā dayāluḿ śaraṇaḿ vrajema

Translation: Alas, how shall I take shelter of one more merciful than He who granted the position of mother to a she-demon [Pūtanā] although she was unfaithful and she prepared deadly poison to be sucked from her breast?

And 

SB 10.21.5

barhāpīḍaḿ naṭa-vara-vapuḥ karṇayoḥ karṇikāraḿ

bibhrad vāsaḥ kanaka-kapiśaḿ vaijayantīḿ ca mālām

randhrān veṇor adhara-sudhayāpūrayan gopa-vṛndair

vṛndāraṇyaḿ sva-pada-ramaṇaḿ prāviśad gīta-kīrtiḥ

TRANSLATION: Wearing a peacock-feather ornament upon His head, blue karṇikāra flowers on His ears, a yellow garment as brilliant as gold, and the Vaijayantī garland, Lord Kṛṣṇa exhibited His transcendental form as the greatest of dancers as He entered the forest of Vṛndāvana, beautifying it with the marks of His footprints. He filled the holes of His flute with the nectar of His lips, and the cowherd boys sang His glories.

Srila Sukadev Goswami hearing the Divine Transcendental Pastimes of the Lord came back and heard Srimad Bhagavatam from his father Veda Vyasa . Srila Sukadeva Goswami further says to Maharaja Parikshit in SB 2.1.10 :

tad ahaḿ te 'bhidhāsyāmi

mahā-pauruṣiko bhavān

yasya śraddadhatām āśu

syān mukunde matiḥ satī

TRANSLATION: That very Śrīmad-Bhāgavatam I shall recite before you because you are the most sincere devotee of Lord Kṛṣṇa. One who gives full attention and respect to hearing Śrīmad-Bhāgavatam achieves unflinching faith in the Supreme Lord, the giver of salvation.