Reading Strong's Real Hebrew dictionary, I discovered that כּלּה kallâh "bride, spouse" < כּלל kâlal "to make perfect". What does a bride have to do with perfection?
כּלל also means the group or the all, as in the word כּל - all.
The bride is the perfect crystalline form of society, she is the paradigm and paragon of the all.
Hence when Hashem brought Chavah to Adam, he adorned her with the 24 adornments (jewels) of a bride (Zohar 1, 48b). But additionally we learn that (Maseches Sofrim 15.5)
"מה כלה מקושטת בכ"ד קישוטין, אף תלמיד חכם צריך להיות בקי בכל כ"ד ספרי תנ"ך.
Just as a bride is adorned with 24 adornments, so too must a talmid chacham be adorned with the 24 books of the scriptures.
So that the beauty of the talmid chacham is derived from the example of the perfect beauty of the bride, because the bride is the perfect form.
Building on my comment above the understanding is that prior to the creation of his wife, Adam was judged as being incomplete, both figuratively and physically.
In Bereishis 2:18 the Torah states:
The LORD G-d said, “It is not good for man to be alone; I will make a (lit. a helper against him) fitting helper for him.”
Ramban (Nachmanadies) writes:
It does not seem that man was created to be the only one in the world and will not give birth to all the creatures male and female, of all flesh were created to establish a seed and also the grass and the tree sowed in them, but it is possible to say that was as the saying goes (see Brachos 61a) "two faces [du partzufin]" were created, they were made to have a nature bringing in the reproductive organs from the male to the female, a strength to give birth....and this second face helps the first in producing children, and G-d saw that it was good as this 'helper' stands before him and he will see and part with him and connect with him as he pleases. And this is what is meant by "I will make him a helper against him" and this is the reason why (G-d upon seeing that Adam was alone) said it was "not good" (and) not to say about him that it is good to be alone, since the act of creation had not yet been fulfilled - this "good" was the fulfilment like I explained with my piece on "And G-d saw that it was good" (1:4).
So it would seem through the creation of Chava/Eve, the first wife; this helped to perfect the creation, it finalised the act and now warranted the appellation of being "good".
This idea is reinforced a few verses later in 2:24 where the Torah writes:
Hence a man leaves his father and mother and clings to his wife, so that they become one flesh.
Rashi clarifies "one flesh" to mean:
The child is formed through both of them, (and their coming together) makes them into one flesh.
The Ramban brings this Rashi and adds:
In my view animals do not cleave to their sexual partners; the male approaches any female it finds and then leaves. For this reason the text says since the female of the adam was a bone of his bones and flesh of his flesh, he cleaved to her and she was in his bosom like his own flesh and he desired her to be constantly with him. As this was so with Adam so was his nature transmitted to his progeny, to make the males, cleaving to their females, leaving their fathers and mothers and regarding their wives as if they were one flesh with them. Similarly, “you are our brother, our flesh (gen.37:27), “to the meat of ones flesh (Lev.18:6), those close in family are called “meat of flesh” and so will leave the “meat” of his father and his mother and their closeness and see that his wife is closer to him than they are. (sefaria translation - not all the Hebrew is there)
So to return to your question, how is a bride also tied with perfection? The answer is that through her union with her husband they now represent a complete creation. In the same way it was not good for man to be alone, and G-d provided a wife for Adam, so too for all spouses, the act of marriage allows them to now become one complete entity.
In addition, building on the Gemara Brachos that was cited in the first Ramban, Adam was initially created both male and female in one body. G-d then split this female part from Adam to create Chava. Thus when a husband and wife get married, through their act of intimacy, they reconnect once more to the primordial creation of mankind by becoming one again, and thus, now represents a sense of perfection.