The 22-year-old from Western Australia braved the blustery conditions at Royal Beroun Golf Club to post a 1-under-par 71, just three behind leader Ana Dawson.
It was a rollercoaster ride for Rudgeley, a rookie on the Ladies European Tour.
Her round on Friday included an eagle on the par-five seventh, birdies on 5, 9 and 10, a bogey on 3 and a triple-bogey on the par-four 14th.
But the winner of the Athena Challenge on the WPGA Tour of Australasia in 2022 is still firmly in the mix and in a tie for 11th.
Dawson, the first Isle of Man player to compete on the LET, made two eagles, three birdies, one bogey and a triple-bogey.
The 22-year-old enjoyed a three-stroke lead on six-under-par after 15 holes before losing a ball on the 16th and running up a triple-bogey seven.
But she battled back to finish with a birdie on the 18th to edge one stroke ahead of four others.
“It was pretty up and down. There were two eagles and a triple, so it was a real mixed bag, but overall I played pretty well, so I’m not going to look too hard into 16 and it was nice to finish strongly, with a birdie on 18,” said Dawson.
Spain’s Ana Peláez Trivino is tied for second with Celine Herbin of France, Ursula Wikstrom (Finland) and Indian Diksha Dagar on three-under-par 69.
New Zealanders Wenyung Keh and Momoka Kobori are tied for sixth place with fellow rookie Alexandra Forsterling, Norwegian Marianne Skarpnord and Sweden’s Linnea Johansson on two-under-par 70.
Peláez Trivino, who has the chance to overtake Aditi Ashok as the top player on the Race to Costa del Sol this weekend, went to the turn in 37 but four birdies in her last five holes saw her come back in 32 as the winds eventually calmed later in the evening.
Wikstrom, who has her 16-year-old son, Erni, caddying for her this week, made her score on the front nine, which she played in 33.
“I surprisingly made a few long putts, which was great, because with the gusty wind it wasn’t easy. I was prepared for rain, but we were lucky it wasn’t raining. I don’t know which is easier, rain or wind,” Wikstrom said.
Earlier in the day, Sweden’s Louise Stahle made a hole-in-one on the 11th using a 7-iron.
Moments earlier, she was recalling the hole-in-one that she recorded on the same hole, in the same round, in the same tournament, last year.
The only difference was she used a 9-iron to make the ace 12 months ago.