We investigate the occurrence and source of modulations in the gain and phase of flame transfer functions (FTF) measured in perfectly premixed, bluff body stabilised CH4/H2 and pure H2 flames. The modulations are shown to be caused by flow disturbances originating from the upstream geometry, in particular the grub screws used to centre the bluffbody, indicative of a more generalised phenomenon of convective wave propagation. Velocity measurements are performed at various locations around the injector dump plane, inside the injector pipe, and in the wake of the bluffbody to provide detailed insight into the flow. Peaks corresponding to natural shedding frequencies of the grub screws appear in the unforced velocity spectra and it is found that the magnitude of these convective modes depends on their location. Flame imaging and PIV measurements show that these disturbances do not show up in the mean velocity and flame shape which appear approximately axisymmetric. However, the urms and vrms fields capture a strong asymmetry due to convective disturbances. To further quantify the role of these convective disturbances, hydrodynamic transfer functions are constructed from the forced cold flow, and similar modulations observed in the FTFs are found. A strong correlation is obtained between the two transfer functions, subsequently, the modulations are shown to be centered on the vortex shedding frequency corresponding to the first convective mode. The reason behind the excitation of the first mode is due to a condition that states that for acoustic-convective interaction to be possible, the shedding (convective) frequency needs to be lower than the cut-off frequency of the flame response. This condition is shown to be more relevant for hydrogen flames compared to methane flames due to their shorter flame lengths and thus increased cut-off frequency.