It seems to me that the any quality study of the White influence on the Blues should be grounded in a good understanding of the characteristics of Black American music and the African roots of Black American music, specifically the Blues.

With regard to the African roots of the Blues, one book I suggest the researcher read is Samuel Charter's "The Roots of The Blues: An African Search" {Boston; London; Marion Boyars, 1981}. Though this book has 14 chapters, I would particularly call the researcher's attention to Chapter 11 "The African Blues Roots". Here's an excerpt from that chapter:

"...It was clear, as I had first realized listening to the griot songs,that they didn't sound much like the blues. The two songs came from different musical idioms. But I could also hear certain traits-like the way of singing and the rhythmic texturing-that were common to each of them. At some point they had perhaps sounded much more alike, but both the griot's music and the music in the southern United States had changed, each of them going in their own direction. The voices themselves had a a great deal of similarity in tone and texture...There was the same kind of tone production, the same forcing of higher notes. If a griot like Jali Nyama Suso had sung in English the sound of his voice would have been difficult to distinguish from an Afro-American singer's. In the gruffness of the lower range and the strong expressiveness of the middle voice I could hear stylistic similarities to singing I had heard in many parts of the South.

The differences came in the structure of the melodies and the accompaniments the griot played...

So I had found some things that related the two musical forms-the style of singing, the occasional use of rhythmic figures, the kind of texturing of the voice and accompanying rhythm. Also the role of the singers in their small communities were similar, and in the rural areas of the South, the blues man performed a much wider range of songs than recordings would suggest. They were their farm's dance band, children's entertainer, gospel singer, and blues man, all rolled into one. The usual name for them was 'songster', and perhaps this comes closer to the Mandingo description of a 'jali' than the term blues man does...

At the same time, though, I found so much that was different. When I listened to [certain griot singers] I was surprised to hear how much Arabic influence there was in the music. The elaborate instrumental flourishes were all more Arabic than African...When the blues first came to the notice of European intellectuals in the 1920s and 1930s ther had been some comments about similarities between the blues and flamenco music but I hadn't taken them seriously because I coudn't see any link between the two styles. It was clear now that the West African musicians had already been influenced by Arabic music just as the gypsy singers and instrumentalists had been along the Mediterranean. The influence hadn't come from the Gypsies to the Mississippi blues men. There had been an earlier Arabic music that had influenced them both. This would also help explain the Portuguese fado-which is often dscribled as a kind of blues..."
[pps 118, 123, 125]

-snip-

There's much more. Quoting sparse excerpts does not do this book justice.