GNSS phase observable-specific signal bias (OSB) corrections are essential for widespread application of precise point positioning with ambiguity resolution (PPP-AR) or PPP-RTK. However, subject to the orbital error effects, conventional undifferenced (UD) model-derived BeiDou System (BDS) real-time (RT) OSB products are usually unsatisfactory. In this study, a novel OSB-generating method assisted by the double-differenced (DD) model is proposed. The reliable integer UD ambiguities are obtained by converting DD ambiguities with given ambiguity datums, by which the RT orbit error effects on ambiguity fixing can be reduced during the OSB extraction and PPP-AR process. Validated using data from two regional sparse GNSS reference networks in Shaanxi, China, and Europe, results show that the proposed method-derived OSB products can improve RT PPP-AR performance effectively. In the Shaanxi network, the narrow-lane ambiguity residuals for BDS-3 within ± 0.25 cycles are improved by 23.1% and 33.2% compared to those using the UD model and Centre National d’Etudes Spatiales (CNES)-derived OSB products, respectively, and the corresponding values are 15.2% and 43.1% in the European network. A centimeter- or even millimeter-level positioning accuracy can be achieved for BDS PPP using the poposed OSB products in both networks. In the kinematic PPP-AR test within the Shanxi network, the mean RMS of the BDS-2/3 fixed solutions in the east, north, and up directions is 0.9, 0.7, and 2.3 cm, with a decrease of 57.1%, 53.3%, and 46.5% compared to that using OSB derived by UD model. The median Time-To-First-Fix (TTFF) is also shortened from 23.8 to 7.5 min.