The Sun lies in the middle of an enormous cavity of a million degree gas, known as the Local Bubble. The Local Bubble is surrounded by a wall of denser neutral and ionized gas. The Local Bubble extends around 100 pc in the plane of Galaxy and hundreds of parsecs vertically, but absorption-line surveys of neutral sodium and singly-ionized calcium have revealed a highly irregular structure and the presence of neutral clouds within an otherwise tenuous and hot gas. We have undertaken an all-sky, European-Iranian survey of the Local Bubble in the absorption of a number of diffuse interstellar bands (DIBs) to offer a novel view of our neighbourhood. Our dedicated campaigns with ESOs New Technology Telescope and the INGs Isaac Newton Telescope comprise high signal-to-noise, medium-resolution spectra, concentrating on the 5780 and 5797 AA bands which trace ionized/irradiated and neutral/shielded environments, respectively; their carriers are unknown but likely to be large carbonaceous molecules. With about 660 sightlines towards early-type stars distributed over distances up to about 200 pc, our data allow us to reconstruct the first ever 3D DIB map of the Local Bubble, which we present here. While we confirm our expectations that the 5780 AA DIB is relatively strong compared to the 5797 AA DIB in hot/irradiated regions such as which prevail within the Local Bubble and its walls, and the opposite is true for cooler/shielded regions beyond the confines of the Local Bubble, we unexpectedly also detect DIB cloudlets inside of the Local Bubble. These results reveal new insight into the structure of the Local Bubble, as well as helping constrain our understanding of the carriers of the DIBs.