We analyse the role of bars in the build-up of central mass concentrations in massive, disc galaxies. Our parent sample consists of 3757 face-on disc galaxies with redshifts between 0.01 and 0.05, selected from the seventh Data Release of the Sloan Digital Sky Survey. 1555 galaxies with bars are identified using the position angle and ellipticity profiles of the i-band light. We compare the ratio of the specific star formation rate measured in the 1–3 kpc central region of the galaxy to that measured for the whole galaxy. Galaxies with strong bars have centrally enhanced star formation; the degree of enhancement depends primarily on the ellipticity of the bar and not on the size of the bar or on the mass or structure of the host galaxy. The fraction of galaxies with strong bars is highest at stellar masses greater than 3 × 1010 M⊙, stellar surface densities less than 3 × 108 M⊙ and concentration indices less than 2.5. In this region of parameter space, galaxies with strong bars either have enhanced central star formation rates, or star formation that is suppressed compared to the mean. This suggests that bars may play a role in the eventual quenching of star formation in galaxies. Only 50 per cent of galaxies with strongly concentrated star formation have strong bars, indicating that other processes such as galaxy interactions also induce central starbursts. We also find that the ratio of the size of the bar to that of the disc depends mainly on the colour of the galaxy, suggesting that the growth and destruction of bars are regulated by gas accretion, as suggested by simulations.