The Galactic bulge holds key information on the early formation history of the Milky Way, but efforts aiming to map its detailed present-day structure have not reached a full consensus. Our goal is to accurately map both the space-varying extinction curve in the bulge's foreground, and the 3-dimensional distribution of its oldest stellar population using RR Lyrae stars as tracers. We find non-standard mean optical-infrared extinction ratios and trace large and coherent variations in the reddening curve, in qualitative agreement with independent findings. We employ an unbiased extinction correction to derive an accurate map of the old Galactic bulge. It is remarkably different from the barred structure traced by red clump stars, and shows subtle features requiring further investigation.