Bauza struck in the 25th, 35th and 44th minutes in Saturday's League One clash at the Liberty Stadium after Paul Anderson had opened the scoring in the 17th minute.
Anderson got the ball rolling when he raced on to a loose ball after a Charlie Daniels mis-kick and his low shot flew past visiting keeper Glenn Morris and into the corner of the net.
Bauza then took centre stage as Jason Scotland held the ball up until the Spaniard arrived to slide home. His second goal came after the Os defence stood still waiting for an offside flag and when it never arrived Morris had to rush out of goal to clear but sent it straight to Bauza who calmly drove into the empty net from 25 yards.
His hat-trick came in fortunate circumstances just before the interval when it struck the crossbar and bounced down onto the line only for the referee's assistant to signal a goal.
Wayne Gray pulled one back in the 63rd minute with a far-post header but the Swans fully deserved to finish off in style.