In this paper, we propose a bias field free Spin Hall Nano Oscillator (SHNO) device with perpendicular-To-plane magnetic anisotropy for alternative computing. Coupled oscillator networks can be used to perform computations such as edge detection of an image, associative computing, etc.That are unsuitable (inefficient) in von-Neumann computing models. Recent experiments on SHNOs have demonstrated their frequency of oscillation in gigahertz range, operating at low input currents. However, in the experiments so far, an external magnetic field is used for the operation of SHNOs. This can be mitigated by using the bias field free SHNO device structure proposed in this work. We also discuss the possibility of operating many 3 terminal SHNOs using a single current source by sharing the Spin Hall Metal (SHM) or Heavy Metal (HM) in an array. Biasing multiple SHNOs using single current source offers high energy efficiency at an array level compared to the conventional biasing technique. We also propose a design technique in which an adaptive external magnetic field is used to address the issue associated with shared heavy metal.