We measured the rotationally resolved infrared spectra of helium solvated methyl fluoride at 3 μm and 10 μm, wherein lies C-H and C-F stretching bands, respectively. The linewidths (FWHM) were found to increase with increasing vibrational energy and range from 0.002 cm-1 in the v3 band (C-F stretch) at ~1047 cm-1, to 0.65 cm-1 in the v4 band (asymmetric C-H stretch) at ~2997 cm-1. In between these two bands we observed the lower and upper components of the Fermi triad bands (ν1/2ν2/2ν5) at ~2859 and ~2961 cm-1. We carried out Stark spectroscopy on the lower band on account of its narrower linewidths (0.04 vs. 0.14 cm-1, respectively). The objective of performing Stark spectroscopy was to see if there is any evidence for a rotational linewidth dependence on the external field strength, due to a reduced difference in between methyl fluorides rotational energy gap and the roton-gap of superfluid helium. We did not find any evidence for such an effect, which we largely attribute to the rotational energy gap not increasing significantly enough by the external field. We point to another molecule (formaldehyde) whose energy levels are predicted to show a more promising response to application of an external field.