'I think it's funny because when I won back in '98, I never even made a trip into the media room until after I won,' Steinhauer said after firing a 6-under 66 in her third round to take a three-shot lead over Juli Inkster, Lorena Ochoa, Karen Stupples and Sophie Gustafson.
'When anyone asks how many tournaments I've won, when I say the British Open, they just assume it was a major,' Steinhauer said.
'I just don't say anything,' she joked.
Saturday, Steinhauer had four birdies to go along with an eagle at the par-5 15th, where she reached the green in two with a 3-wood and then drained a 50-foot putt.
The eagle helped her shoot a five-under on the back, which moved Steinhauer to 7-under-par 209 for the championship.
Inkster, who led after both of the first two rounds, had her fortunes reversed by a disastrous round.
Taking a step back in her quest for the Super Career Grand Slam, Inkster had two double-bogeys and two bogeys on the way to a 74. All of her poor scores came on holes where she found bunkers.
'That was pretty much my day,' said Inkster, who has won seven majors but never a Women's British and now finds herself three back.
'I am a little bit of a stewer, but I am still in a really good position for tomorrow. The weather is supposed to be a little bit nasty, so that will be good and we will see what happens.'
The other players in the chase pack reached 4-under 212 by breaking par Saturday: Ochoa fired a 65, the low round of the tournament, while former British winners Gustafson and Stupples shot 69 and 70, respectively.
Ochoa's bogey-free round included back-to-back birdies from the first and four birdies on the back nine, including the 18th. Her best career finish at a major was a runner-up at this year's Kraft Nabisco Championship, when she lost a playoff to Karrie Webb.
'I knew I needed a low round to [get into] a position for Sunday,' said Ochoa, a two-time winner this year, 'and I really wanted to take advantage that I was playing in the morning with nice conditions and I'm glad I did.'
World No. 1 Annika Sorenstam sits seven shots back at even-par after a third-round 73, her highest score this week.
Sixteen-year-old Michelle Wie, meanwhile, followed consecutive 74s with a 72 on Saturday and is tied for 32nd place at plus-4.
Wie was assessed a two-stroke penalty in the second round for grounding her club in a bunker. Otherwise, she would be a little closer to her fourth top-five finish at this year's majors.
'A lot can happen tomorrow,' Wie said. 'This is what happened today and that is what happened yesterday. Tomorrow is a whole new day. I feel like I am playing well enough to shoot a really low score here.'
Cristie Kerr shot a 66 and Natalie Gulbis had a 67 to move into a share of sixth place with Candie Kung (71) at 4-under 212.
Reigning LPGA Rookie of the Year Paula Creamer (73) is among a group of five other players tied with Sorenstam for 15th place.