Ross McKnight’s converted try put County 7-0 up before Lewis McNamara got five points for the Bulls, but George Arnott’s seven pointer put the home side 14-5 ahead.
Grant Stewart scored next for the Bulls before Logan Trotter’s converted effort put Stirling 21-12 up at the break.
Tries from Cam Jones and Joe Knight earned the Bulls a four try bonus point in the second half, but John McKenna and Walter Fifita tries gave County five points.
Watsonians Rugby are second in the table and have two wins from two after a late penalty try came on the back of scores from Ryan Daley, Murray Scott and skipper Cal Davies to give them a 29-20 bonus point win at The Greenyards against the Southern Knights.
Nathan Chamberlain and Billy Wara scored the winless Knights’ tries.
They knew a bonus point triumph at Dumbreck would be enough and they made sure early on, securing the four try bonus before half-time.
Gala won 36-25 at Dundee Rugby, but Heriot’s beat the Maroons to the top spot.
Cartha’s loss means they are relegated along with Boroughmuir.