Context. An unidentified emission line at 3.55 keV was recently detected in X-ray spectra of clusters of galaxies. The line has been discussed as a possible decay signature of 7.1 keV sterile neutrinos, which have been proposed as a dark matter (DM) candidate. Aims. We aim to further constrain the line strength and its implied mixing angle under the assumption that all DM is made of sterile neutrinos. Methods. The X-ray observations of the Limiting Window (LW) towards the Galactic bulge (GB) offer a unique dataset for exploring DM lines. We characterise the systematic uncertainties of the observation and the fitted models with simulated X-ray spectra. In addition, we discuss uncertainties of indirect DM column density constraints towards the GB to understand systematic uncertainties in the assumed DM mass in the field of view of the observation. Results. We find tight constraints on the allowed flux for an additional line at 3.55 keV with a positive (∼1.5σ) best fit value F_X^{3.55 keV} ≈ (4.5 ± 3.5) × 10⁻⁷ cts cm⁻² s⁻¹ . This would translate into a mixing angle of sin²(2Θ) ≈ (2.3 ± 1.8) × 10⁻¹¹ which, while consistent with some recent results, is in tension with earlier detections. Conclusions. We used a very deep dataset with well understood systematic uncertainties to derive tight constraints on the mixing angle of a 7.1 keV sterile neutrino DM candidate. The results highlight that the inner Milky Way will be a good target for DM searches with upcoming missions like eROSITA, XRISM, and ATHENA.