We report far-IR Herschel observations obtained between 70 $\mu$m and 500 $\mu$m of two star-forming dusty condensations, B1-bS and B1-bN, in the B1 region of the Perseus star-forming cloud. In the Western part of the Perseus cloud, B1-bS is the only source detected in all of the 6 PACS and SPIRE photometric bands without being visible in the Spitzer map at 24 $\mu$m. B1-bN is clearly detected between 100 $\mu$m and 250 $\mu$m. We have fitted the spectral energy distributions of these sources to derive their physical properties, and find that a simple greybody model fails to reproduce the observed SEDs. At least a two-component model, consisting of a central source surrounded by a dusty envelope is required. The properties derived from the fit, however, suggest that the central source is not a Class 0 object. We then conclude that while B1-bS and B1-bN appear to be more evolved than a pre-stellar core, the best-fit models suggest that their central objects are younger than a Class 0 source. Hence, they may be good candidates to be examples of the first hydrostatic core phase. The projected distance between B1-bS and B1-bN is a few Jeans lengths. If their physical separation is close to this value, this pair would allow the mutual interactions between two forming stars at a very early stage of their evolution to be studied.Read less <