The Pole, chasing a third French Open title in four years, got off to a sluggish start on a windy afternoon on Philippe-Chatrier court.
She had beaten the Spaniard in under an hour, losing just one game, at this year's Australian Open but Swiatek had a less than perfect run-up to Paris, retiring from her Italian Open quarter-final after suffering a thigh injury two weeks ago.
The triple Grand Slam winner was broken twice in her first three service games as a determined Bucsa, ranked 70th in the world, mixed it up and initially succeeded in throwing her opponent off balance.
But the top seed heeded that wake-up call towards the business end of the set and broke back to seal it.
The Pole, who began her 61st week at the top of the WTA rankings and is the favourite in Paris, snatched another break at the start of the second set with a thundering crosscourt forehand winner and never looked back.
She made amends for her first-set wobble with a bagel.
