Basically, Baha'i scriptures describes that, in every Major faith, there is a Promised One, who was to come to bring peace and re-establish the original teachings of those Faiths.
Thus we see, for example, Christ said He comes again. Buddha said another Buhdda comes again, same as other faiths such as Islam Shia, which believe in 2 promised Ones, and also Hinduism has its own promised One to come at the end of Age.
Baha'u'llah claimed to be that Figure that was promised by all major religions.
The date can be consistantly from Islamic and Christian and Jewish Bible, to the exact same date.
As regards to Buddhism, a few Baha'i Scholars have done some research, which I will put a couple of Quotes here:
"In Mahayana sources there are many more prophecies relating to the Maitreya Buddha. One of these is that found in the Mahasannipata sutra (Ta-tsi-king, see Cowell et al. 115-6n), in which it is prophesied that the Maitreya Buddha would come after five epochs of five hundred years each from the time of Gautama Buddha. This period of 2,500 years was completed in 1956 C.E. according to the traditional Buddhist calendar. Also of importance from the Bahá'í viewpoint is the name of the Mahayana savior figure Amitabha, who is considered to preside over a Pure Land (Sukhavati) to the west of India. Bahá'ís point out the similarity between this name (which may be translated as Light of the Infinite) and that of Bahá'u'lláh (which may be translated as Glory or Light of God), who came from a land to the west of India. There is also a parallel between the repetition of the name of Amitabha in many Buddhist Pure Land sects, and the repetition of the Greatest Name (q.v.) in Bahá'í prayer (see "Prayer.4.b"). To detail fully the Bahá'í interpretation of how the various Buddhist prophecies indicate the coming of Bahá'u'lláh is impossible in an article of this nature. In brief, it may be stated that the Buddhist prophecy that the Maitreya Buddha will inaugurate an era of universal peace and tranquillity is regarded by Bahá'ís as having been fulfilled by Bahá'u'lláh's advent and teachings on world peace."
Buddhism and the Baha'i Faith