Washable underwear only beats disposables if it actually survives the laundry. The routine is simple: rinse cold right after wearing, machine wash cold on a gentle cycle, and tumble dry low or hang to dry.
Two things shorten the life of the absorbent core more than anything else: bleach and fabric softener. Bleach breaks down the fibers that hold liquid, and softener coats them so they stop absorbing at all. Skip both, always.
With a rotation of five to seven pairs and this routine, each pair is rated for 200+ washes — easily a year or more of daily use.