Yes, scanning b/w film with a dedicated film scanner does sometimes seem to increase/accentuate the grain, especially so compared with traditional printing. However, this "graininess" depends also very much on the film being used, as well as on your development and scanner settings. You could try the chromogenig b/w films like Ilfrod XP-2 or Kodak BW400, to start with. If you prefer traditional b/W films instead, Ive had nice results e.g. with Agfa APX100 or Neopan Acros in Rodinal. Thin negs normally scan better.
Try also scanning the b/w film as color neg, with GEM on 1 and ICE off, of course.
Try to get a very low contrast scan and adjust that later with Levels & Curves in PS.
Finally, use Google. There's plenty of threads on this topic already out there.