The Bulls chief previously expressed his ‘immense disappointment’ last season’s clash at Odsal Stadium was called off due to coronavirus cases within the Sheffield camp.
His comments came after the Eagles embarrassed Bradford on the opening day of the 2021 season when they ran in 10 tries to win 50-12.
As per rules set by the RFL, rugby league’s governing body, part-time clubs such as Sheffield were not required to find a rearranged date for cancelled games.
Yet a Bradford statement read: “When clubs are only 30 miles away we would certainly look to fulfil the match.
"We are a professional sport and fulfilling fixtures has to be our fundamental priority.”
Aston refused to budge, however, and told The Star: "Nobody has ever seen anything like it (the 2021 season) and the players’ welfare is something we shouldn’t play lip service with.
"That’s why I’m adamant we won’t play these games (against Bradford and York City Knights) because I wouldn’t risk putting players out three times a week.
"It’s crazy if you want to do that.”
The two sides met on Sunday in Round Two of the 2022 Betfred Championship season, with underdogs Sheffield running out 28-14 winners to pick up their first points of the campaign.
Aston described the performance of his players as ‘outstanding’ and added: "Sometimes you get what you deserve. All the negative publicity, their chairman having a go at our chairman, it was nice to go there (and win).
"Actions speak louder than words and we spoke very loud.”
Another trip to West Yorkshire awaits the Eagles this weekend.
They are set to take on a ‘desperate’ Dewsbury Rams side on Sunday, who have lost their opening two games.
He said: “The standard we set against Bradford was very, very high. They raised the bar and people now expect us to go there and get the result.
"If we get the performance right the result will look after itself, there’s no doubt about that."
Aston revealed Sheffield have targeted two wins from their first four matches and said a win against Dewsbury would lift some pressure ahead of next weekend’s trip to Batley, who have won their opening two fixtures.