Roberto Martinez's side have not lost in their last 12 home Premier League games - last tasting a league defeat at Goodison in December 2012, when they lost 2-1 to Chelsea.
That is the longest current unbeaten home run in the top flight and the feat has been built around a solid defence, with Everton keeping seven clean sheets from their last eight matches in their own back yard.
Martinez's men sit seventh, with their solitary defeat coming against Manchester City before the international break.
After starting the campaign with three draws, Everton then won three in a row before going down 3-1 at the Etihad Stadium.
Martinez feels his side have made a good start but challenged them to keep improving, starting with the visit of Hull.
"We're pleased with the start but it's just a start and we need to keep on growing," he said.
"What we need to do now is carry on developing a way of playing that is going to be consistent and strong throughout the season.
"I feel the squad is ready to do that. That's our next target, to concentrate on Saturday and make sure we carry on with the level of performance we have shown throughout this season."
Martinez has something of an injury crisis to contend with after Darron Gibson ruptured his anterior cruciate ligament while on international duty with the Republic of Ireland.
Gibson joins Antolin Alcaraz (groin), Apostolos Vellios (knock) and Steven Pienaar (knee) on the treatment table, although the latter could return for the trip to Aston Villa on October 26.
Hull will fancy their chances of taking something from the game despite Everton's formidable record at home, with Bruce's charges unbeaten in their last four Premier League games.
Draws against Cardiff City and Aston Villa came either side of victories over Newcastle United and West Ham, leaving Hull just a point and a place behind Everton in the table.
Bruce has also received a boost with the news that top scorer Robbie Brady is in line for a return to action.
Brady, who has four goals in all competitions this season, missed the 0-0 draw with Villa due to a hernia injury but Bruce confirmed he is likely to play some part against Everton.
Hull's only other injury absentees are James Chester (hamstring) and Robert Koren (ankle), with all of the their internationals returning to club duty unscathed.
"Thankfully it looks as though everybody is coming back okay," Bruce told the club's official website.
"We're still waiting for Ahmed Elmohamady, Gedo and Maynor Figueroa to get back but having spoken with medical staff, everything seems ok so that is the most important thing."
