"It wasn't fazed by us and kept following us ... I kept thinking, 'If this bear attacks, how am I going to cover my children and protect my children?'" she told KUTV.
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Peachey captured her family's reaction on video as the bear followed the couple and their three children -- ages 1 to 6 -- for approximately 20 minutes, sometimes trailing the group by only a few feet.
"Can we play dead now?" her oldest son calmly asks in the video.
"Walk faster please," Peachey responds.
She said the bear had blocked the path to the parking lot, so the family had to continue walking up the Whistler trail.
"It was a little nerve-racking when there's a bear following you, but it was kind of our only option."
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Mom scoops up toddler as she chases bear in backyard
Peachey, a former health care worker, is now an outdoor family lifestyle influencer, so she said she felt well equipped to handle this situation.
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"I knew that we just had to stay calm, and I had to keep reminding my kids, 'Don't run, don't run. That will spook the bear and make it worse.'"
After about a half-mile, the bear trailed off, and Peachey said the animal never acted belligerently.
She said she later found out officials had closed off that hiking area several times because of this bear's increasing aggressive behavior.
Peachey added that she teaches her kids to respect the wild, and this won't change the way they experience the outdoors. To her, the risk is worth the reward.
"You're in their territory, and even if you do all the things you're supposed to do, they might not care. They still might want to keep coming the direction they're going or still come after you, so it's a really good reminder to be cautious when you're out there."
Experts say that anyone who encounters a bear in the wild should avoid screaming, running and making eye contact. Instead, stay calm, back away slowly, and make yourself look as big as possible.