The match against Dover will take place on February 6, which means the scheduled home game against Tranmere Rovers will be moved.
In Bower’s view, the “ridiculous” decision to put the Tranmere game on the weekend of the third-round matches in the FA Trophy has the potential to damage the Lions and is exceptionally demanding of fans.
Guiseley now face a daunting run of six weeks without a home game.
Bower said: “At the minute we have so many away games at a time where fans are having to fork out week in and week out to go on away trips.
“They have been unbelievable for us.
“For the ones that make it to Dover it will be a monumental effort really, because of the away games we have got. It’s ridiculous fixture planning that we are having to cope with at the minute.
“That Trophy game replaces the Tranmere home game and the two Saturdays either side of that fixture we have been given matches away from home.
“We are going to go six weeks with consecutive Saturday away games.
“For a part-time club that relies on income from Saturday home games, that’s an absolute joke.
“The way it’s been worked out, our fans and our club are the ones who are going to have to pay for it more than anyone else and we have not been looked after at all.”
Guiseley face a trip of 272 miles to play Dover. Bower admits it’s one of the tougher games his side could have been handed in the third-round draw, not least because Dover are fourth in the National League.
However, the Lions did manage a 0-0 draw on their trip to the Crabble Athletic Ground earlier this campaign, which gives Bower hope.
He continued: “It’s not the kindest of draws.
“The first thing you want is a home tie. You don’t want to be travelling too far. We have some distance to travel. We are playing one of the best teams left in the competition.
“It’s probably about as bad as it could get for us in terms of a draw, but we went down there and got a draw in the league, plus we have competed against all sides in our league.
“We will go down there and look to get a result.
“If it means bringing them up for a replay, then we will do that, or we will go for a win.”
Bower is also convinced Dover will not be particularly happy with the draw either.
“They would have been looking at it and hoping that they got someone from a lower league as well,” he said.
“Hopefully we can go there with a game plan and try and win.
“We certainly have the players in our dressing room that are capable of doing that.
“So we will go down there and try to get through.”
Elsewhere in the draw, Halifax Town will face Chester at The Shay, assuming they can get past Barrow.
Bradford Park Avenue or Nantwich Town have been drawn against Stourbridge.
Tonight in the Evo-Stik First Division North, Farsley host Harrogate Railway Athletic, while Garforth play Thackley in the NCEL Premier Division.
Glasshoughton Welfare are in NCEL League Cup action against Pickering Town.