Sarah Graham's block of an attempted clearance put a bouncing ball in front of Bayliss, who volleyed past the keeper from near the penalty spot.
A header from a corner kick in the 33rd minute gave Bayliss her second goal and United a 2-0 halftime lead.
In the 59th minute, Chelsea Simpson ran on to a through ball but was denied by a good save from Campion goalkeeper Olivia Whitfield.
But the dynamic Simpson proved uncontainable four minutes later. She chased a bouncing ball from halfway and finished cleanly.
Riverina were merciless in their win against Marist Thistle.
Lizzie Hall and Briar McLeely scored four goals each, Jayde Neal and Grace Levy, three each, and Dara Mulrooney and Olivia Rogers, one each.
In the game at the Rectory, Tyler Andrews gave Bohemians the halftime lead with a long-range shot that dropped out of the sun late.
Morgan Andrews' second-half goal came off strong midfield build-up play.
Goalkeeper Dana Kingsbeer was Bohemians' player of the day.
This Sunday, Bohemians play Riverina at Anzac Park, Marist Thistle play United at Childers Road Reserve, and Campion College play Gisborne Girls' High School at Campion.
Riverina are scheduled to play United once more this season, on October 4. The way things are going, the result of that game could decide the women's club championship.