Aims: The relative cosmic variance (σv) is a fundamental source of uncertainty in pencil-beam surveys and, as a particular case of count-in-cell statistics, can be used to estimate the bias between galaxies and their underlying dark-matter distribution. Our goal is to test the significance of the clustering information encoded in the σv measured in the ALHAMBRA survey. Methods: We measure the cosmic variance of several galaxy populations selected with B-band luminosity at 0.35 ≤ z< 1.05 as the intrinsic dispersion in the number density distribution derived from the 48 ALHAMBRA subfields. We compare the observational σv with the cosmic variance of the dark matter expected from the theory, σv,dm. This provides an estimation of the galaxy bias b. Results: The galaxy bias from the cosmic variance is in excellent agreement with the bias estimated by two-point correlation function analysis in ALHAMBRA. This holds for different redshift bins, for red and blue subsamples, and for several B-band luminosity selections. We find that b increases with the B-band luminosity and the redshift, as expected from previous work. Moreover, red galaxies have a larger bias than blue galaxies, with a relative bias of brel = 1.4 ± 0.2. Conclusions: Our results demonstrate that the cosmic variance measured in ALHAMBRA is due to the clustering of galaxies and can be used to characterise the σv affecting pencil-beam surveys. In addition, it can also be used to estimate the galaxy bias b from a method independent of correlation functions. Based on observations collected at the German-Spanish Astronomical Center, Calar Alto, jointly operated by the Max-Planck-Institut für Astronomie (MPIA) at Heidelberg and the Instituto de Astrofísica de Andalucía (CSIC).