Following Saturday's goalless home draw against Southampton - where captain Grant Holt saw a stoppage-time penalty saved - the Canaries are nine points clear of trouble heading into the final nine games.
However, Bunn insists there is a bit more hard work ahead before anyone at Carrow Road can start talking about a third season in the Premier League.
"We don't see ourselves as safe. I think we need a couple more wins and then we will be okay," said Bunn, who is hoping to retain his place in the side when England goalkeeper John Ruddy is back in contention later this month after recovery from his long injury lay-off following thigh surgery.
"We have got some crucial games coming up. Sunderland is a winnable game so hopefully we can look forward to that and get the three points, then against Wigan too.
"They are games against teams around us, so our main aim is not to lose those games, try to take a point away from home and win our home games.
"If we do that then we will be all right."