We present Giant Meterwave Radio Telescope 1280-MHz radio continuum observations and follow-up optical studies of the disc and nuclear star formation in a sample of low-luminosity bulgeless galaxies. The main aim is to understand bulge formation and overall disc evolution in these late-type galaxies. We detected radio continuum from five of the 12 galaxies in our sample; the emission is mainly associated with disc star formation. Only two of the detected galaxies had extended radio emission; the others had patchy disc emission. In the former two galaxies, NGC 3445 and NGC 4027, the radio continuum is associated with star formation triggered by tidal interactions with nearby companion galaxies. We did follow-up Hα imaging and nuclear spectroscopy of both galaxies using the Himalayan Chandra Telescope. The Hα emission is mainly associated with the strong spiral arms. The nuclear spectra indicate ongoing nuclear star formation in NGC 3445 and NGC 4027 which may be associated with nuclear star clusters. No obvious signs of active galactic nuclei activity were detected. Although nearly bulgeless, both galaxies appear to have central oval distortions in the R-band images; these could represent pseudo-bulges that may later evolve into large bulges. We thus conclude that tidal interactions are an important means of bulge formation and disc evolution in bulgeless galaxies; without such triggers these galaxies appear to be low in star formation and overall disc evolution.