The 27-year-old, who moved to Carrow Road from Blackburn Rovers over the summer, saved a penalty during what was only his second appearance for the side in Wednesday's 2-1 win over Tottenham Hotspur in the Capital One Cup.
"When you come to a new club you just have to take your chance when you are given it and I think I did that," Bunn said.
"It was great to save the penalty and get the win. I just have to keep working hard now and maybe push [John Ruddy] because he's a fantastic player and I get on really well with him."
The Canaries return to Premier League action on Saturday when they host Stoke City.