Since Baha'u'llah had revealed as much at least as early as the Kitab-i-Aqdas (which had been published in Baha'u'llah's liftetime around 1873 significantly before His passing in 1892), I would assume the Baha'is had already been turning toward His direction for their obligatory prayer.
"O people of the Bayán! Fear ye the Most Merciful and consider what He hath revealed in another passage. He said: "The Qiblih is indeed He Whom God will make manifest; whenever He moveth, it moveth, until He shall come to rest." Thus was it set down by the Supreme Ordainer when He desired to make mention of this Most Great Beauty. Meditate on this, O people, and be not of them that wander distraught in the wilderness of error. If ye reject Him at the bidding of your idle fancies, where then is the Qiblih to which ye will turn, O assemblage of the heedless? Ponder ye this verse, and judge equitably before God, that haply ye may glean the pearls of mysteries from the ocean that surgeth in My Name, the All-Glorious, the Most High."
(Bahá'u'lláh, Kitáb-i-Aqdas, par. 137)
As to the reason for the change, Muhammad also changed The Qiblih to Mecca, and Baha'u'llah indicated that this had no other purpose except to "test and prove the peoples of the world":
Know verily that the purpose underlying all these symbolic terms and abstruse allusions, which emanate from the Revealers of God's holy Cause, hath been to test and prove the peoples of the world; that thereby the earth of the pure and illuminated hearts may be known from the perishable and barren soil. From time immemorial such hath been the way of God amidst His creatures, and to this testify the records of the sacred books.
And likewise, reflect upon the revealed verse concerning the "Qiblih."1 When Muhammad, the Sun of Prophethood, had fled from the dayspring of Bathá1 unto Yathrib,2 He continued to turn His face, while praying, unto Jerusalem, the holy city, until the time when the Jews began to utter unseemly words against Him — words which if mentioned would ill befit these pages and would weary the reader. Muhammad strongly resented these words. Whilst, wrapt in meditation and wonder, He was gazing toward heaven, He heard the kindly Voice of Gabriel, saying: "We behold Thee from above, turning Thy face to heaven; but We will have Thee turn to a Qiblih which shall please Thee."3 On a subsequent day, when the Prophet, together with His companions, was offering the noontide prayer, and had already performed two of the prescribed Rik'ats,4 the Voice of Gabriel was heard again: "Turn Thou Thy face towards the sacred Mosque."5,6 In the midst of that same prayer, Muhammad suddenly turned His face away from Jerusalem and faced the Ka'bih. Whereupon, a profound dismay seized suddenly the companions of the Prophet. Their faith was shaken severely. So great was their alarm, that many of them, discontinuing their prayer, apostatized their faith. Verily, God caused not this turmoil but to test and prove His servants. Otherwise, He, the ideal King, could easily have left the Qiblih unchanged, and could have caused Jerusalem to remain the Point of Adoration unto His Dispensation, thereby withholding not from that holy city the distinction of acceptance which had been conferred upon it.
(Kitab-i-Iqan, pars. 53-54)
As far as the reason for the rapidity
of the change of the laws of the Bab, the Baha'i Writings indicate that on one level, this is a mystery, and on another, that the laws of the Bab had fulfilled their designated revolutionary purpose in clearing away the old in preparation for Baha'u'llah's coming:
The Bábí Dispensation was being brought to its close (not prematurely but in its own appointed time), and was yielding its destined fruit and revealing its ultimate purpose--the birth of the Mission of Bahá'u'lláh. In this most dark and dreadful hour a New Light was about to break in glory on Persia's somber horizon. As a result of what was in fact an evolving, ripening process, the most momentous if not the most spectacular stage in the Heroic Age of the Faith was now about to open.
During nine years, as foretold by the Báb Himself, swiftly, mysteriously and irresistibly the embryonic Faith conceived by Him had been developing until, at the fixed hour, the burden of the promised Cause of God was cast amidst the gloom and agony of the Síyáh-Chál of Tihrán. "Behold," Bahá'u'lláh Himself, years later, testified, in refutation of the claims of those who had rejected the validity of His mission following so closely upon that of the Báb, "how immediately upon the completion of the ninth year of this wondrous, this most holy and merciful Dispensation, the requisite number of pure, of wholly consecrated and sanctified souls has been most secretly consummated." "That so brief an interval," He, moreover has asserted, "should have separated this most mighty and wondrous Revelation from Mine own previous Manifestation is a secret that no man can unravel, and a mystery such as no mind can fathom. Its duration had been foreordained."
St. John the Divine had himself, with reference to these two successive Revelations, clearly prophesied: "The second woe is past; and, behold the third woe cometh quickly." "This third woe," `Abdu'l-Bahá, commenting upon this verse, has explained, "is the day of the Manifestation of Bahá'u'lláh, the Day of God, and it is near to the day of the appearance of the Báb." "All the peoples of the world," He moreover has asserted, "are awaiting two Manifestations, Who must be contemporaneous; all wait for the fulfillment of this promise." And again: "The essential fact is that all are promised two Manifestations, Who will come one following on the other." Shaykh Ahmad-i-Ahsá'í, that luminous star of Divine guidance who had so clearly perceived, before the year sixty, the approaching glory of Bahá'u'lláh, and laid stress upon "the twin Revelations which are to follow each other in rapid succession," had, on his part, made this significant statement regarding the approaching hour of that supreme Revelation, in an epistle addressed in his own hand to Siyyid Kázim: "The mystery of this Cause must needs be made manifest, and the secret of this Message must needs be divulged. I can say no more. I can appoint no time. His Cause will be made known after Hin (68)."
(Shoghi Effendi, God Passes By, pp. 92-93)
Shoghi Effendi continues on to pose the question of what the greatness of Baha'u'llah's own Revelation must be given the rapid change to a new Dispensation.
"What, we may well inquire at this juncture, were the nature and implications of that Revelation which, manifesting itself so soon after the Declaration of the Báb, abolished, at one stroke, the Dispensation which that Faith had so newly proclaimed, and upheld, with such vehemence and force, the Divine authority of its Author? What, we may well pause to consider, were the claims of Him Who, Himself a disciple of the Báb, had, at such an early stage, regarded Himself as empowered to abrogate the Law identified with His beloved Master?"
(ibid, p. 93)
Note 109 in the Kitab-i-Aqdas provides some further context: http://bahai-library.com/writings/bahau ... ml#note109