We simulate the spin wave (SW) dynamics in ring structures and obtain the $ω − k$ dispersion relations corresponding to the output waveguide. Different bias field configurations affect the transfer of SW power from one arm of the structure to the other arm. To this end, we show that circular or radial bias fields are more suitable for energy transfer across the ring than the conventional horizontal bias field $H_{x}$. The SW dispersion shows that modes excited, when the bias field is along the ring radius, are almost 10 dB higher in power when compared to the modal power in the case of $H_{x}$. This is also corroborated by the SW energy density in the receiving stub.