We explore variations of the dust extinction law of the Milky Way by selecting stars from the Swift/UVOT Serendipitous Source Catalogue, cross-matched with Gaia DR2 and 2MASS to produce a sample of 10 452 stars out to ~4 kpc with photometry covering a wide spectral window. The near ultraviolet passbands optimally encompass the 2175 Å bump, so that we can simultaneously fit the net extinction, quoted in the V band (AV), the steepness of the wavelength dependence (δ), and the bump strength (Eb). The methodology compares the observed magnitudes with theoretical stellar atmospheres from the models of Coelho. Significant correlations are found between these parameters, related to variations in dust composition that are complementary to similar scaling relations found in the more complex dust attenuation law of galaxies - that also depend on the distribution of dust among the stellar populations within the galaxy. We recover the strong anticorrelation between AV and Galactic latitude, as well as a weaker bump strength at higher extinction. δ is also found to correlate with latitude, with steeper laws towards the Galactic plane. Our results suggest that variations in the attenuation law of galaxies cannot be fully explained by dust geometry.