According to this article by the DC Policy Center, a part of Bloomingdale/LeDroit Park is a food desert.
I have copied this article's DC food desert map and exploded the part that covers Bloomingdale and LeDroit Park. I circled the identified food desert marked in pink.
It looks like the area bounded by 2nd Street NW, V Street NW, 4th Street NW and T Street NW -- in Bloomingdale and LeDroit Park -- is considered a food desert.
And now you know that.