'Here comes the bride' implies that the wedding guests are gathered before the bride arrives. That everyone has been waiting for the bride, and then she shows up, usually accompanied by her father. All eyes turn towards her arrival, and 'here comes the bride'.
The Wedding March by Robert Wagner colloquially known as 'Here comes the bride' became popular when Victoria, Princess Royal, the daughter of Queen Victoria, used it for her wedding in 1858.
In modern times, the father leads his daughter, the bride, up the aisle, to 'give her away' - this is where traditionally the woman passes out of the care and control of her father, into that of her husband - and the music 'here comes the bride' usually accompanies that part of the ceremony.
In modern weddings this tradition is sometimes done away with, along with the tradition of the woman promising to 'obey' her husband (men did not traditionally promise to 'obey' the wife), because modern women may find these traditions objectionable.
So in modern weddings, bride and groom may enter together, or be found by the guests already present in some setting - so then there is no 'here comes the bride' moment of 'arrival'.
Unfortunately, marriage, and weddings have a very dark history, for women, that is glossed over and not usually acknowledged in our normal romantic thoughts of 'the happy day' and 'here comes the bride' - and even that piece of music, from Lohengrin is followed by a scene in the opera where the groom kills off 5 of the wedding guests, abandons Elsa without consummating the marriage, and leaves on a boat pulled by a swan. It sounds like a reversed nightmare wedding gone wrong, doesn't it!
Bride kidnapping is, sadly, another way in which the bride, even today, can still 'arrive'.
See the 'forced marriage' section of this wiki:
Women throughout history have been effectively, and literally, sold into marriage, by their families or father, and raped by their (forced) new husband, to a degree that may make your jaw drop, if you allow yourself to look into it. A dowry or payment was made, making women chattels who effectively 'belonged' to their husbands and did not 'exist' in society without a husband, meaning they 'had to' have one.
If this seems distant to you, in a modern western society like the UK or USA, then look at India, which still has arranged marriages and wedding dowry payments from the brides family that go not to the bride herself but to her 'new family'. 'Here comes the bride' - with her bounty.
Auctioning brides. According to Herodotus, 484–c. 425 BC, in Babylon, auctions of women for marriage were held annually. The auctions began with the woman the auctioneer considered to be the most beautiful and progressed to the least. It was considered illegal to allow a daughter to be auctioned independently, outside of the 'market'. In this case, all the young women were herded into one place, and sold - not 'here comes the bride', but 'here are the brides'. This is not by the way an isolated incident, it was commonplace, and widespread, and not just in Babylon.