How do I analyze 'the bride within the bridal dress had withered like the dress and like the flowers and had no brightness left but The brightness...

One the most famous of Dickens’s creations, Miss Havisham sits in her wedding dress with the clocks all stopped at 20 minutes to 9:00, the exact time on her wedding day when she discovered she had been jilted. The line you quote comes at the end of a long passage of description in which Pip recalls the first time he laid his eyes on this interesting woman.

To analyze this paasage, we must imagine Pip as a child entering Miss Havisham's big room for the first time. Although it's daytime, the room is lit with candles. At first, as he comes closer to Miss Havisham he thinks she is dressed in white:

She was dressed in rich materials,—satins, and lace, and silks,—all of white. Her shoes were white. And she had a long white veil dependent from her hair, and she had bridal flowers in her hair, but her hair was white. Some bright jewels sparkled on her neck and on her hands, and some other jewels lay sparkling on the table.

From afar, she looks beautiful, but as Pip comes closer, he--and we as the readers--see she is no longer beautiful at all. Everything she wears is yellowed, and her bridal gown "withered." We can understand the gown as a symbol of Miss Havisham herself, also yellowed and withered with age.

As Pip draws closer, he senses  that all is not as he had expected. Things that to his mind "ought to be white" are not. Other oddities include that fact that Miss Havisham wears only one shoe. These outward representations in clothing reflect a soul that has also "withered," but the young Pip doesn't yet have the analytical abilities to figure this out.

In this passage, the adult Pip presents himself as the young child who sees, absorbs and doesn't fully comprehend how damaging Miss Havisham's inability to move on from her trauma will be. That the adult Pip narrates this scene is indicated by this line:  "It was not in the first few moments that I saw all these things, though I saw more of them in the first moments than might be supposed."

Settings, including clothing, are an important way Dickens establishes what his characters are like. Through her clothes, we see the dismal effects of loneliness and isolation on this woman. But we note too that all is not withered: Miss Havisham's eyes are bright. It's significant that Dicken's repeats the word "brightness" twice. This suggests that his "withered" creation still has life inside her despite the decay all around her, and this brightness, as unnatural as the "wax candles" that light the room, foreshadows the trouble she will cause.