We present a systematic study of the shape of the dust attenuation curve in star-forming galaxies from the far ultraviolet to the near infrared (0.15-2microns), as a function of specific star formation rate (sSFR) and axis ratio (b/a), for galaxies with and without a significant bulge. Our sample comprises 23,000 (15,000) galaxies with a median redshift of 0.07, with photometric entries in the SDSS, UKIDSS-LAS (and GALEX-AIS) survey catalogues and emission line measurements from the SDSS spectroscopic survey. We develop a new pair-matching technique to isolate the dust attenuation curves from the stellar continuum emission. The main results are: (i) the slope of the attenuation curve in the optical varies weakly with sSFR, strongly with b/a, and is significantly steeper than the Milky Way extinction law in bulge-dominated galaxies; (ii) the NIR slope is constant, and matches the slope of the Milky Way extinction law; (iii) the UV has a slope change consistent with a dust bump at 2175AA which is evident in all samples and varies strongly in strength with b/a in the bulge-dominated sample; (iv) there is a strong increase in emission line-to-continuum dust attenuation with both decreasing sSFR and increasing b/a; (v) radial gradients in dust attenuation increase strongly with increasing sSFR, and the presence of a bulge does not alter the strength of the gradients. These results are consistent with the picture in which young stars are surrounded by dense `birth clouds' with low covering factor which disperse on timescales of ~1e7 years and the diffuse interstellar dust is distributed in a centrally concentrated disk with a smaller scaleheight than the older stars that contribute the majority of the red and NIR light. [abridged]

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