Two goals from Lisa Naalsund either side of half-time were enough to grab all three points at Leigh Sports Village.
The visitors set up defensively, making it hard to break through, but the Reds’ boss was delighted with how his side played.
Skinner spoke to the media after the game about the commitment of the players, the importance of Naalsund and why Geyse brings something different.
THE GAME WAS ALWAYS UNDER CONTROL
“Bristol City organise the block, with difficult limited spaces. You're going to have to maximise the space. If you look at our goal, it's a perfect way of getting beyond the midfield line.