The West Riding club finished seventh in National League North, a position that until this season would have meant missing out on extending their season.
But last summer’s change to competition rules mean the play-offs in the fifth and sixth tiers of English football now feature six teams, as opposed to the previous four, in a series of one-off meetings.
“We feel a little bit like Denmark in the 1992 European Championships,” said Bower, ahead of tackling Kidderminster Harriers tonight.
“Reaching the play-offs never really felt on until last Thursday, when North Ferriby scored against Spennymoor (the team Avenue pipped to seventh) in what was their game in hand on us.
“That 1-1 draw left it in our hands for the first time. That is what I mean when I say we feel like Denmark, who were called back off the beach to play in the Euros due to Yugoslavia being kicked out.
“It means there isn’t any pressure on us. Five of the six teams in the play-offs started the season targeting promotion, whereas we were being tipped for relegation.”
Avenue head to Aggborough for the second time in five days knowing third-placed Brackley Town await the victors in Sunday’s qualifying semi-finals.
Runners-up Harrogate Town will host the winners of tonight’s other eliminating tie between Stockport County and Chorley at Edgeley Park. The final takes place on May 13.
Bradford’s place in the play-offs was sealed by a five-game winning finale to the regular campaign, capped by a dramatic last-minute winner from Adam Boyes at Kidderminster.
Harrogate, Kidderminster and Brackley all succumbed to Bower’s men during a run-in that saw Spennymoor pipped to the final place on goal difference.
“The league has been so tight this season that anyone who gets into the play-offs has to be respected,” added Bower.
“We have come with a late run. Often, that can be crucial in the play-offs as you have the momentum. We will just have to wait and see. Kidderminster will bring a few players back in who were rested last Saturday against us but we have nothing to lose.”