The Shaymen have reached the play-offs in two of the last three seasons, just missing out in the other campaign, under previous boss Pete Wild.
His replacement Chris Millington has been tasked with something of a rebuilding job this summer having lost captain Niall Maher, top-scorer Billy Waters and first-team regulars Tyrell Warren, Tom Bradbury and Kieran Green.
But Bosomworth feels the club can maintain their status as promotion contenders.
"We'll have to wait and see how the new additions to the squad settle in," he told the Halifax Courier.
"There will be a settling in period, so it might take a few games for things to settle down, but hopefully we've identified the right players to come and do a good job, and give an opportunity to good, up and coming players who want to progress their careers.
"We'd obviously love promotion. Are we going to get the number one position? Who knows, but we'd certainly like to think we've got a chance of reaching the play-offs.
"But there are some big hitters in the league, we all know who they are, and you have to compete with them as best they can.
"That's the nature of the beast, we had that last season and we were in second or third for a large part of the season only to finish fourth right at the end."
Town's 2021-22 season had barely finished when Wild departed for League Two side Barrow, kicking off a hectic off season at The Shay.
"It's one of the most difficult close seasons we've had if truth be told, obviously starting with the loss of the manager," Bosomworth said.
"We had an incredible amount of applications, it must be said, but the first port of call was to interview Chris, which we did through a proper process.
"Sometimes it's a more difficult interview to do when you know somebody already, but a full interview process was gone through and Chris came through it with flying colours.
"He's very committed, very knowledgeable, understands what we're about as a club, understands the restrictions we have to operate under but also the opportunities that presents.
"He's a really diligent guy who wants to give 110 per cent and prove himself as a number one."
On Wild's departure, Bosomworth said: "There was no ill will whatsoever, Pete had done a great job for us and at the end of the day he felt he wanted to move into League Two.
"Possibly had we got promoted we wouldn't have had those discussions but he felt he wanted that opportunity, and he's taken it."
Bosomworth says it was a huge plus to be able to retain the rest of the backroom staff though.
"When there's a managerial change you don't know what the consequences of that are - we might have lost Chris Millington or others within the backroom team," said the chairman.
"But thankfully we've retained everybody - the physio, the goalkeeping coach, the kit man and obviously Chris himself, so that's really good.
"It helps provide ongoing continuity and the players who are still with us know what we're about and understand what we're trying to do.
"We just want to try and build on that.
"Of course, we'll miss Pete, he did ever so well. But as they say, the King is dead, long live the King, so we move on."
Bosomworth, speaking to the Courier before the sale of Kieran Green to Grimsby, said the club was frustrated to lose so many of their first-team players this summer, but said their hands are tied if bigger clubs come in for them.
"Niall was with us for four years, Billy came to us on a one-year contract which we tried to extend halfway through the season but he wanted to leave his options open until the end of the season," Bosomworth said.
"He's obviously explored those options, to go into League Two and to follow his previous manager.
"We all have the same frustrations, obviously we wanted to keep Niall, Tyrell Warren and others, but if bigger clubs come in for them, you have to accept that, particularly when they're out of contract. There's not a lot you can do about it."
Bosomworth says there has been an increase in the playing budget this season, and says the club is "fine" financially.
"Don't get me wrong, it's not a huge increase, but having to bring certain players in, we wanted key players in key positions," he said.
"Any fees generated through the transfer market will also be utilised within the squad."
Some Shaymen fans have been critical of the club's prudent approach, arguing Town should speculate to accumulate more if they want to secure promotion.
"Well you've got have the money to speculate with first," said Bosomworth.
The chairman is pragmatic about maintaining a promotion push in what looks like yet another highly competitive season ahead on the National League.
"Obviously the two clubs that came down from the EFL, Scunthorpe United and Oldham Athletic, will benefit from a parachute payment which is probably bigger than our whole playing budget," he said. "So that's a distinct advantage for those two clubs.
"You've then obviously got the likes of Wrexham, who are probably going to have 10 league players in their squad, Chesterfield, Notts County, Solihull.
"Torquay, Dagenham and Redbridge and Boreham Wood will all be vying for positions, then you have the likes of York City, don't rule them out just because they've come up from the National League North, they might get stuck in early doors.
"Then you've got unknown quantities like Dorking Wanderers and Maidstone.
"We say this every year, and so do all the clubs, it's an unrelenting league. You need a bit of luck and you need a bit of finance and a bit of everything to help yourselves get out of the league.
"The benchmark is looking at Wrexham, who are the longest serving club in this league, but even with their resources last season it still didn't guarantee them promotion.
"I'm sure they'll be very thereabouts this season, but it's taken them a long time, even though they get bigger crowds and have more revenue.
"It's an unrelenting league but you have to approach it with an open mind and a positive attitude, and have confidence in what you do and how you do it.
"Not every signing will be a success, but some might surprise you."
The Shaymen have now finished in the National League play-offs three times since they reformed in 2008, the latest of which was last season when they were knocked out by Chesterfield.
"I thought we'd a great chance (of promotion) last season, probably what caught up with us was some injuries right at the end and a bit of fatigue by having a reasonably tight, small squad," Bosomworth said.
"Whilst I appreciate Chesterfield had injuries in that play-off game I think we were probably five or six players light at the time.
"And it hurt us, so we didn't get to the second game, which would've been at Solihull.
"But to be fair, Grimsby were outstanding, and won what were in effect three away ties."
One issue that seems to crop up season after season at The Shay is the pitch.
"Apparently it's looking pretty good," said Bosomworth.
"I was sent a photo to it prior to a recent Halifax Panthers game.
On whether he expected issues to arise with the surface again this season, Bosomworth said: "It depends whether we're lucky with the weather and whether the pitch is draining correctly.
"Heavy rain and rugby league isn't a great recipe, but I'm not blaming the rugby league club for that, you just don't want it bucketing it down on a Sunday when the rugby team are playing, which makes it hard to keep it in good condition.
"Hopefully there will be a solution to it.
"We had hoped there was going to be a solution to it this summer, which is why we've played all our pre-season games either away from home or behind-closed-doors.
"There was a change of plan, and we'll look to see if it's something that can be done either by the end of next season or the season after."
Despite the challenges, Bosomworth is still enjoying running the club as he prepares to embark on his 15th season
"Yeah, of course. It's a challenge and it's hard balancing the books, but it is what it is.
"Our costs have gone up again but it's no good moaning about it, we've got what we've got and we've got to make the best of it, and we will do."
And long-term, Bosomworth says he is committed to his role as chairman.
"Yeah, of course, we're doing the best job that we can within the resources available to us," he said.
"If we can get the crowds, then great, but you need continued success to get the crowds to come on a more regular basis I guess, but that's what we need.
"If we were to get crowds of 3,000 plus, it would change the dynamic a bit.
"Wrexham are getting 9,000 to 10,000, so were Stockport. The revenues coming through the turnstiles with that are huge.
"We will work within the confines we have to do the best job that we can, and to give ourselves that chance of promotion."