We study the clustering of galaxies as function of luminosity and redshift in the range 0.35 < z < 1.25 using data from the Advanced Large Homogeneous Area Medium-Band Redshift Astronomical (ALHAMBRA) survey. The ALHAMBRA data used in this work cover 2.38 deg2 in seven independent fields, after applying a detailed angular selection mask, with accurate photometric redshifts, σz ≲ 0.014(1 + z), down to IAB < 24. Given the depth of the survey, we select samples in B-band luminosity down to Lth ≃ 0.16L* at z = 0.9. We measure the real-space clustering using the projected correlation function, accounting for photometric redshifts uncertainties. We infer the galaxy bias, and study its evolution with luminosity. We study the effect of sample variance, and confirm earlier results that the Cosmic Evolution Survey (COSMOS) and European Large Area ISO Survey North 1 (ELAIS-N1) fields are dominated by the presence of large structures. For the intermediate and bright samples, Lmed ≳ 0.6L*, we obtain a strong dependence of bias on luminosity, in agreement with previous results at similar redshift. We are able to extend this study to fainter luminosities, where we obtain an almost flat relation, similar to that observed at low redshift. Regarding the evolution of bias with redshift, our results suggest that the different galaxy populations studied reside in haloes covering a range in mass between log10[Mh/( h-1 M⊙)] ≳ 11.5 for samples with Lmed ≃ 0.3L* and log10[Mh/( h-1 M⊙)] ≳ 13.0 for samples with Lmed ≃ 2L*, with typical occupation numbers in the range of ˜1-3 galaxies per halo.