Question
Did Bhishma attain Swarga or Vaikuntha?
Answer
Your enquiry is about whether Bhishma attained Swarga-Loka or Vaikuntha. And as mentioned in Srimad Bhagavata Purana he became one with Shree Hari and Mahabharata's Svargarohanika Parva he was present in Swarga.
There is description of Bhishma asking the leave of Shree Krishna to leave his body in Mahabhrata - Anushasana Parva - Bhishma-Swargarohana Parva , when he was laying in his death bed and when the right time to depart came Bhishma talked to Shree Krishna and said to him that with his grace he will attain a supreme abode. P. 395
स मां त्ववनुजानीहि कृष्ण मोक्षे कलेवरं |
त्वयाहं समनुज्ञातो गच्छेयं परमां गतिम् || 45 ||Do thou, O Krishna, grant me leave, I shall cast off my body. Permitted by thee, I shall attain to the highest end!'
Upon that Shree Krishna granted him the leave and said to him that he will attain to the status of the Vasus.
अनुजानामि भीष्म त्वां वसून प्राप्नुहि पार्थिव |
न तेsस्ति वृजिनं किञ्चिदिह्लोके महाद्युते ||46 ||"Vasudeva said, 'I give thee leave, O Bhishma! Do thou, O king, attain to the status of the Vasus, O thou of great splendour, thou hast not been guilty of a single transgression in this world.
Now coming to main part of answer.
Further ,there is a story in the next chapter i.e. Chapter No. 168 Of Anushasana Parva-Bhishma-Swargarohana Parva of goddess Ganga the great river indulging in lamentations about her son Bhishma's death from the hands of Shikhandi . Shree Krishna then assured her that her son fought a great battle and there was nobody like him and no one could have defeated him in the battle and he was killed by Arjuna and not by Shikhandi. And then Shree Krishna himself told to goddess Ganga that Bhishma has gone to swarga or heaven as mentioned in below shlokas two times.
भिष्मं हि कुरुशार्दुल्मुद्यतेषुं महारणे ||33 ||
न शक्त: संयुगे हन्तु साक्षादपि शतक्रतु: |
स्वछ्न्दतस्तव सुतो गतः स्वर्गं शुभानने ||34 ||P. 397 Do not yield to grief, O thou of beautiful features! Without doubt, thy son has gone to the highest region of felicity! He was one of the Vasus of great energy. Through a curse, O thou of beautiful features, he had to take birth among men. It behoveth thee not to grieve for him. Agreeably to Kshatriya duties, he was slain by Dhananjaya on the field of battle while engaged in battle. He has not been slain, O goddess, by Sikhandin. The very chief of the celestials himself could not slay Bhishma in battle when he stood with stretched bow in hand. O thou of beautiful face, thy son has, in felicity, gone to heaven. All the gods assembled together could not slay him in battle. Do not, therefore, O goddess Ganga, grieve for that son of Kuru's race. He was one of the Vasus, O goddess! Thy son has gone to heaven. Let the fever of thy heart be dispelled.'
Further if we look - Bhishma was a Kshatriya and he fought the battle according to Kshatriya dharma and died in the battlefield of Kurukshetra , by the law " those Kshatriyas who died at the battlefield according to prescribed law attained Swarga" , like all those he also gone to swarga.
Now coming to your Srimad Bhagavatam quote where it is said that Bhishma became merged with Shree Hari. That means he concentrated on Krishna as supreme Brahman , he went into Nirvikalpa Samadhi or highest stage of meditation where all his activities were focused upon Supreme Brahman. The verses has to be interpreted in this way as mentioned in purport by Swami Prabhupada.
कृष्ण एवं भगवति मनोवाग्दृष्टिवृत्तिभिः
आत्मन्यात्मानमावेश्य सोऽन्तःश्वास उपारमत् ॥ SB .1.9.43 ॥kṛṣṇa evaṁ bhagavati mano-vāg-dṛṣṭi-vṛttibhiḥ
ātmany ātmānam āveśya so ’ntaḥśvāsa upāramatSūta Gosvāmī said: Thus Bhīṣmadeva merged himself in the Supersoul, Lord Śrī Kṛṣṇa, the Supreme Personality of Godhead, with his mind, speech, sight and actions, and thus he became silent, and his breathing stopped.
Purport -The stage attained by Bhīṣmadeva while quitting his material body is called nirvikalpa-samādhi because he merged his self into thinking of the Lord and his mind into remembering His different activities. He chanted the glories of the Lord, and by his sight he began to see the Lord personally present before him, and thus all his activities became concentrated upon the Lord without deviation.
In the chapter of Bhishma-Swargarohana Parva the way with which Bhishma became dead is also mentioned. It is said that his pranas went up through piercing his Brahmarandhra (crown of the head) and went up towards heaven .
P. 396 The life-breaths, restrained and unable to escape through any of the outlets, at last pierced through the crown of the head and proceeded upwards to heaven. The celestial kettle-drums began to play and floral showers were rained down. The Siddhas and regenerate Rishis, filled with delight, exclaimed, 'Excellent, Excellent!' 'The life-breaths of Bhishma, piercing through the crown of his head, shot up through the welkin like a large meteor and soon became invisible
So according to Mahabharata Bhishma did not became one with Krishna but his soul went up to Swarga.
In conclusion:- Bhishma did not attain Vasu-Loka but he became one of the Vasus as he was originally was and took birth on earth by curse of Sage Vashistha. So he merged with Vasus and attain swarga. So Mahabharata, Svargarohanika Parva is correct.
Bhishma merged with Vasus , his original form and attain Swarga as mentioned by Shree Krishna himself in Mahabharata. And the Bhagavatam narration is equally correct but has to be understood by a different way.
Note: “The question: Did Bhishma attain Swarga or Vaikuntha?” is licensed by Stack Exchange Inc (https://hinduism.stackexchange.com/); user contributions licensed under CC BY-SA.