The 28-year-old has been a consistent performer for Stuart Hooper's side for several seasons and was rewarded with a Test debut against Italy last October.
Despite facing stiff competition for the England number two shirt in Jamie George and Luke Cowan-Dickie, Dunn is confident he can add to his three caps.
“I still want to play for England, and I still want to be the best hooker in the country and that's what I'm trying to do,” he said.
“I think the day you give up trying to achieve something like that is the day you probably get replaced. As the cliche goes if you play well for your club then international selection takes care of itself.
“I've just got to keep putting my hand up and see how it goes.”
Bath finished seventh in the Premiership last season, 19 points off the play-off places.
But Dunn is confident the west country outfit can turn things around this season.
“We want to be in the play-offs, and I think we can,” he said. “We've definitely got the potential to do it. We just need to polish up a few bits.
“We've got the squad, we've got the coaching, we've got the ethos and we've got the culture.
“It's impossible to put it down to one thing because rugby is a complicated game.
“For me clarity is massive for where we are going. What are we and how do we play?
“I think we've got that now. It obviously takes time but if we are given time, I think we can achieve that.”
By STEFFAN THOMAS