The Prophet’s dream about marrying ‘Aa’ishah

The hadeeth to which you refer was reported by Imaam al-Bukhaari (may
Allaah have mercy on him) in his Saheeh from Aaishah (may Allaah be
pleased with her), who said that the Prophet
(peace and blessings of Allaah be upon him)
said to her: You were shown to me twice in a dream. I saw you in a piece of silk
(i.e., he saw her image on a piece of silk, or he saw her wearing a silken garment). I was
told, This is your wife, so unveil her, and it was you. I said: if this dream
is from Allaah then it will come to pass.

(Saheeh al-Bukhaari,
3606).

In his commentary on this hadeeth, Ibn Hajar (may Allaah
have mercy on him) said: This dream came after his mission had started, and it was a
wahy (revelation) that had implications in real life. (Its implication was that he did
indeed marry her later on). His words and it was you indicate that he had seen
her before and knew what she looked like. (See Fath al-Baari)

There is nothing in the hadeeth to indicate that his marriage to
Aaishah was as a result of that dream. The Prophet
(peace and blessings of
Allaah be upon him) asked her father for her hand in marriage, and her father Abu Bakr
gave her in marriage, in the usual fashion, as is indicated in the following hadeeth:

Urwah reported that the Prophet
(peace and blessings of
Allaah be upon him) asked Abu Bakr for Aaishahs hand in marriage, and
Abu Bakr said to him: But I am your brother. He said: You are my brother
according to the religion and Book of Allaah (i.e., my brother in Islam), and she is
permissible for me (to marry). (Bukhaari, 4691).

In his commentary Ibn Hajar (may Allaah have mercy on him) said:
Ibn Abi Aasim reported via Yahyaa ibn Abd al-Rahmaan ibn Haatib from
Aaishah that the Prophet
(peace and blessings of Allaah be upon him) sent
Khawlah bint Hakeem to Abu Bakr to ask for Aaishahs hand in marriage.
Abu Bakr asked her, Is she right for him? Because she is the daughter of my
brother. Khawlah went back and mentioned this to the Prophet
(peace and blessings
of Allaah be upon him). He told her: Go back and tell him: You are my brother
in Islam, and your daughter is right for me. She went back to Abu Bakr and
told him, and he said: Call the Messenger of Allaah
(peace and blessings of Allaah
be upon him). So he came and the marriage was performed.

The phrase You are my brother according to the religion and Book
of Allaah (i.e., my brother in Islam) was referring to the aayah (interpretation of
the meaning): The believers are nothing else than brothers (in Islamic
religion) [al-Hujuraat 49:10] and other similar aayaat. The phrase
she is permissible for me (to marry) means it is permissible to marry her even
though she is the brothers daughter, because the kind of brotherhood that would
prevent such a marriage is the brotherhood of descent (same parent) or of radaaah
(by being breastfed in infancy by the same woman), not the brotherhood of faith.

As regards the woman to whom the Prophets marriage was arranged
in heaven, as it were, by Allaah, and not in the customary fashion, this was Zaynab bint
Jahsh (may Allaah be pleased with her), as is indicated by the hadeeth of Anas (may Allaah
be pleased with him), who said: Zaynab used to boast (to her co-wives) about how she
had got married to the Prophet
(peace and blessings of Allaah be upon him), saying:
Your families arranged your marriages but Allaah arranged my marriage from above the
seven heavens. (al-Bukhaari, 6870). No other wife except Zaynab was married to
the Prophet
(peace and blessings of Allaah be upon him) in such a unique fashion;
Aaishahs marriage was arranged as described in the reports quoted above.
May Allaah reward you with good for your question. And Allaah knows best.