To date, there is clear experimental evidence that gold-coated tilted fiber Bragg gratings (TFBGs) are highly sensitive plasmonic biosensors that provide temperature-compensated detection of analytes at concentrations in the picomolar range. As most optical biosensors, they bring an evanescent wave in the surrounding medium, which makes them sensitive to both surface refractive index variations (= the useful biosensing signal) and to bulk refractive index changes (= the non-useful signal for biosensing). This dual sensitivity makes them prone to drift. In this work, we study partially gold-coated TFBGs around their cross-section. These gratings present the ability to discriminate both volume and surface refractive index changes, which is interesting in biosensing to enhance the signal-to-noise ratio. The effects induced in the TFBGs transmitted amplitude spectra were analyzed for surrounding refractive index (SRI) changes in the range 1.3360–1.3370. Then, the gold film was biofunctionalized with human epidermal growth factor receptor (HER2) aptamers using thiol chemistry. The detection of HER2 proteins (a relevant cancer biomarker) at 10−9 g/mL, 10−8 g/mL and 10−6 g/mL demonstrated the advantage to identify environmental perturbations through the bare area of the TFBGs, which is left not functionalized. The non-specific drifts that could exist in samples are eliminated and a wavelength shift only related to the surface modification is obtained.