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Steve Meehan's men began their continental campaign with a heartbreaking home defeat to last season's beaten finalists Biarritz Olympique two months ago, prompting critics to suggest their European adventure was effectively over before it had really begun.
But a bonus-point win over Aironi in Italy sees them sit second in Pool 4 and Wilson says they won't be travelling to Ravenhill short on confidence.
"Bath's always been a good place to be," said Wilson, who starts Saturday's encounter in Northern Ireland at tight-head prop.
"We're still confident that we can pull out some wins if we start playing well. We haven't been that far away and we just need to start getting a few things right. If we do that, I'm sure we'll start winning and start playing well.
"Heads haven't dropped in any way at all. You've just got to keep on being positive and keep on believing in yourselves day in, day out. We've just got to concentrate on doing all the right things in training. We've said all the right things and we just need to back it up on the day.
"With the right attitude and by trying hard in training, hopefully we'll turn the screw and start a run like we did last year when we didn't play well until after Christmas."
Although their Heineken Cup campaign had been dealt a fatal blow prior to that upturn in form last term, Bath's remarkable change in fortunes saw them move from a relegation battle to a top-four finish in the English Premiership.
Their expansive style of play won plenty of plaudits as Bath transformed themselves into the form team in England with 11 wins in 12 domestic fixtures between December and May.
But while it was the backs who stole the show during that fantastic run, Wilson knows it's the forwards who will have to turn on the style if Bath are to leave Ravenhill with a crucial win this weekend.
"Any victory is normally built on the pack," added Wilson, who says Bath are keen to avenge last season's double defeat to the Ulstermen.
"You need quick clean ball and if you get quick clean ball going forward, you'll probably win the game - it's as simple as that.
"Ulster have got a good pack and that's where we'll try and be competitive. They've got big, physical guys, they're good in the scrum and good in the lineout as well.
"The defeats last year were both gutting, really. Most of their success came from their pack - they got some good go forward and that's exactly what we'll try and get this year.
"We need to make sure the backs get front-foot ball. That's what we've been trying to do in training, just get a bit more dominance in the forwards in terms of carrying off the nine and the 10 and trying to set a good platform for the backs.
"If we concentrate on those things, do what we want to do and get everything right, that's all you can ask. If you work harder than the opposition, you should win if you don't make too many mistakes."
Wilson knows the back-to-back clashes with the team who picked up Europe's most sought after prize a year after Bath's sole triumph will have a major impact on who challenges Biarritz for a quarter-final spot.
Lose both games and the dream is all but over for another year. Lose one and Bath face a real uphill task. End the month with two European wins and suddenly reaching the knockout stages looks a distinct possibility.
It's the type of scenario that some players would shy away from, but Wilson isn't one of those. Having spent the majority of the autumn as an England replacement, the 24-year-old is desperate to play a major role in getting Bath's season back on track.
"I'm itching to play. I feel in good shape and I'm quite fresh. It was good to be involved with England. I got probably 60 minutes against Samoa so I enjoyed that game and I feel fit and fresh. I feel like I've picked up quite a bit from England, learnt a bit and got a bit of experience.
"These are important games, obviously. There's a lot at stake. We need them to push on in the Heineken Cup. We need to win both those games and we'll be massively up for it. But they will be as well, and they're going well this year."
