The reality star says he and his new love sneak around for secret meetings

Credit: Bob D'Amico/ABC

Brad Womack is so madly in love, he’s acting like a kid again.

“I call this woman probably 20 times a day. I really am like a high school sophomore,” Womack tells PEOPLE of the woman he chooses on this season of The Bachelor – whose identity remains top secret, as the ABC show, filmed late last year, now airs.

“I’m very much in love, head over heels,” he says. “So, I call and text. I’m doing the whole high school thing. I see her about once or twice a month. It’s under lock and key, of course. It’s not nearly enough.”

Sneaking around to get a glimpse of each other can be a logistical challenge, to say the least. “It’s wild. Different locations all across the country. It’s crazy,” says the Austin, Texas, bar owner, 38. “But it’s well worth it. I would travel to Antarctica to see this woman.”

While he can’t give too many hints about the woman’s identity, Womack does say he felt drawn to her early on, though he worked hard to give all of the women a fair chance.

“I’m a true believer in instant connections,” he says. “Around our first date or so – and I’m not even saying one-on-one or group [date] – I kind of started knowing. I just knew. But – and I promise you I mean this – I carried every relationship through to the very end.”

He adds: “There’s no denying that I felt it very, very quickly … Once I fall, I just know. I fall very hard, and it happened. It happened. But I did use every second wisely, I promise you.”

While he can’t elaborate on his choice, don’t count out Michelle or Emily just because they have kids.

“I’ve always wanted a family. I thought, okay, if a relationship works out with either Michelle or Emily, the only two with children, so be it. That’s an instant family,” Womack says. “I’m a guy [for whom] true love is all encompassing. Meaning, if she has a child, I would love that child … just like she was my own.”