Is it stated in Shia Books that Abu Bakr accompanied the Prophet SAW in the migration from Makkah to Madina and was with him in the cave of Thawr?
We do not have any authentic evidence neither in our books nor in Sunni books that Abu Bakr accompanied the Prophet Muhammad (SAWA) in his migration from Makkah to Madina. On the contrary, we have in authentic Sunni books that Abu Bakr was not with the Prophet during that journey as you can see in Al-Bidayah Wal Nihayah by Ibn Katheer narrating from Ibn Jareer al-Tabari. (Al-Bidayah Wal Nihayah , Vol 3, Page 219) and also Al-Seerah al-Nabawiyyah by Ibn Katheer , V. 2 , Page 236).
The person who was accompanying the Prophet (SAWA) was a travel guide who knows the roads of the desert between Makkah and Madina by the name of Abdullah Ibn Orayqit Ibn Bakr عبد الله بن أريقط بن بكر (Mukhtasar Tareekh Dimashq by Ibn Asaakir , V. 13, P. 35).
Some people changed the name from Ibn Bakr to Abu Bakr.
The narration that Abu Bakr was with the Prophet in the cave of Thawr and the spider covered the cave's entrance is fabricated and it has got similar story in the Jewish stories as it as been admitted by leading Sunni scholars. (Tafseer al-Qurtubi, V. 13, P. 346).
In the well known book (Saheeh al-Bukhari (1:170) narrating from Ibn Umar that Abu Bakr and Umar and other well known persons migrated to Madina before the Prophet and used to pray in Masjid Qiba behind Saalim Mawla Abi Huthaifah. Also, there is in Saheeh al-Bukhari 8:115), a narration from Abdullah Ibn Umar that Saalim Mawla Abi Huthaifa used to lead in prayers Muslims including Abu Bakr, Umar, Abu Salamah, Zaidand Aamir Ibn Rabee'ah. That was before the arrival of the Prophet to Madina.
Al-Haakim Al-Neesaboori who is a leading Sunni scholar in Hadeeth has narrated that the Prophet migrated from makkah alone and Abu Bakr was not with him (Al-Mustadrak Alal Saheehayn, 3:133).
There is book written on this subject by Shaikh Najaah al-Taa'ee.
Wassalam.