The Jamaican striker, who joined the club in summer, now has eight goals in 14 games this season.
City conceded an own goal to open the scoring but recovered well to give a dominant performance, something Taylor was very pleased with.
"We handled that well, we had a setback, the character was good, we remained calm knowing we’d get back in the game at some point and there were two bits of quality from Bunny Shaw," he said.
"Second half we controlled the game, we retained possession really well and created good opportunities.
"If we’re nitpicking we probably should’ve scored more but we have to be happy and we are really pleased to get through."
It was Bunny's first start since October and she certainly made an impact on her team and manager.
"It's great, considering she's been off with Covid," Taylor said.
"We were limited in terms of what we could do with her and her minutes, we checked the stats at half-time and decided to keep her out there for another 15 minutes just to help Ellen White as well because her work load has been high in those first three games.
"I'm pleased because we saw a glimpse of what Bunny’s all about before Christmas and now we’re seeing more of the player we want to see in Bunny. It was a good performance from her.
"She came up against a tough opponent, the girl who played left center back was a physical player but Bunny is physical as well.
"Sometimes it's difficult to get the edge but the first goal she made from nothing, sometimes that's what you need. You can't always score the perfect goal. It was a good pull back and finish, she had a big influence on game.
"There’s loads more to come from Bunny, the more she plays with the players, the more she’s involved with the team the better, obviously again similar to Caroline, it’s been difficult because she’s missed a few weeks on return from the Christmas break due to Covid.
"She made a positive effect before Christmas and on Saturday. Great to get two goals, tonight so really pleased with her."
CITY V ARSENAL
Tickets for City's first home league game of 2022 - a crunch FA WSL clash against Arsenal - are now on sale.
Don't miss your chance to cheer on Gareth Taylor's side on Sunday 23 January. Kick-off 18:45 at the Academy Stadium.