Using fully kinetic Particle-In-Cell (PIC) modelling we investigate how magnetic reconnection responds to a varying guide field in one of the inflow regions. We find that the reconnection rate varies significantly when the orientation of the magnetic field changes between being strictly antiparallel and having a guide field. These variations are fairly consistent with the scaling relation for asymmetric reconnection developed by Cassak and Shay (2007). However, the rate is also found to be non-linearly modulated by changes in the ion inflow velocity. The spatio-temporal change in the inflow velocity arises as the magnetic forces reconfigure to regions of different magnetic field strengths. The variations in the inflow magnetic field configuration allow for different gradients in the magnetic field, leading to asymmetries in the magnetic tension force. By momentum conservation, this facilitates asymmetries in the inflow velocity, which in turn affects the flux transport into the reconnection site. The outflow is found to be less laminar when the inflow varies, and various signatures of the inflow variations are identified in the outflow.