Context. The so-called bump spectral signature observable on interstellar extinction curves, peaking at 217.5 nm, is commonly assigned to π* ← π transitions from carbonaceous carriers, but the exact nature of the carbonaceous carriers remains debated. Aims. To constrain the chemical structures associated with the bump carriers, we record and compare the UV spectra of a large variety of carbonaceous molecules to this interstellar feature. Methods. Large carbonaceous molecules, such as polycyclic aromatic hydrocarbons (PAHs), were produced by a combustion process stabilized at low pressure under rich flame conditions. Species were extracted and probed through resonance enhanced multiphoton ionization spectroscopy coupled to a time-of-flight mass spectrometer. Masses and absorption profiles of the carbonaceous molecules were measured, and their spectra were compared to the bump feature. Results. Species showing a specific mass progression starting at mass 128 u visible up to mass 394 u with a characteristic progression of +14 u present a common electronic absorption band profile peaking asymptotically around 220 nm. The first masses were assigned to a naphthalene C10H8 molecule and two of its derivatives: C10H7CH3 and C10H7C2H5. The mass progression of +14 u is explained by successive H atom substitutions by CH3 functional groups. This mass distribution was thus assigned to naphthalene derivatives with large aliphatic carbon substitution. This derivative family shows an electronic band assigned to S3 ← S0 transitions involving electron promotion within the π aromatic orbitals of the naphathlene chromophore. More importantly, after a few substitutions, the position of the band converges asymptotically to a value close to the interstellar bump signature, independent of the molecule size. Conclusions. Based on the asymptotic behavior of the larger members in the species distribution, a similar band position is expected from double aromatic ring substructures within hydrogenated amorphous carbons (HACs). Similar to the conclusions of previous works, we find substituted naphthalene units as substructures of interstellar HACs to be good candidates as carriers of the bump feature.