The 22-year-old beat Bencic 6-3, 1-6, 6-3 on Tuesday, advancing to the last four after failing to progress beyond the fourth round in her previous six attempts.
With the win, she also became the youngest American to reach the women's singles semi-finals in Miami since Serena Williams in 2004.
"I think sometimes I can get impostor syndrome," Gauff told reporters.
"Even when they are saying my accomplishments when I walk on or during the warm-up, it doesn't feel like me and I'm like, 'Oh, actually, you do have a good career'.
"But it doesn't feel like that sometimes. When you're working on things, and especially with my serve, it just feels like I shouldn't be where I am. But tennis doesn't lie, the ball doesn't lie, so I just have to believe in myself."
Gauff, a two-time Grand Slam champion, said her coach has been focused on helping her build confidence.
"At moments, I believe in it, and other moments, I don't. I'm just trying to believe in it more," she said.
Gauff will face Czech Karolina Muchova in the semi-finals on Thursday, having won all five of their previous meetings.