Bradford assay can be used for measuring of the concentration of all sorts of proteins: total, soluble or specific (in case if its pure). Under the acidic conditions of the assay all proteins are getting denatured anyway.
In general, soluble proteins are those which can make enough hydrogen bonds with water and therefore are able to stay in the solution being thermodynamically comfortable. Insoluble proteins are too hydrophobic, and in order to cover hydrophobic regions exposed to water they use other hydrophobic molecules around - other hydrophobic proteins. They tend to clump together, clumps grow in size, and eventually precipitate. Precipitation can be enhanced by centrifugation. For most applications, precipitated proteins are as good as dead, and that is why people often measure only soluble proteins. In other words, every total protein contain soluble and insoluble proteins, and they can be quickly separated using centrifuge.
If you want to measure only soluble protein using Bradford, you have to centrifuge your sample and use the supernatant. For the total protein content, use the sample as is.
Bradford reagent is mainly 85% phosphoric acid plus Coomassie Blue.
Here is a recipe for it:
https://www.usbio.net/protocols/bradfords-reagent
In case you want to make it yourself, make sure the Coomassie Blue is completely dissolved in the methanol; otherwise you get lumps in your Bradford reagent causing noisy results.