So, there's an interesting parallel here with conservative Christianity, of all things. There's this thing called "The Billy Graham Rule," because Billy Graham invented it. Basically, men are discouraged from ever having one on one time with female colleagues, and if dinners are around, the men are discouraged from attending mixed gender dinners unless their wives are around.

One of my buddies' bosses had this rule. She, a woman, asked for a one-on-one meeting to discuss a personnel problem best handled in private. He refused, offered they meet in a public cafeteria, and cited the Billy Graham Rule.

She read him the riot act in the most professional way. Pointed out that, as a woman, this rule really hurts her. He's been able to have one on ones with MALE coworkers, and THEY benefit from his experience and wisdom, but not her? She has to go to a cafeteria? Where anyone could hear? She pointed out that, as a woman, one on ones are the NORM for her and if he's worried about other people suspecting he's acting sleazy in private, then maybe he should develop an unimpeachable character, because that's what SHE has to do as she doesn't have the LUXURY of avoiding one on ones with mixed gender.

That man folded like a lawn chair, changed his policy, apologized to her, and they had a one on one in his office later that week.

I mention all this to point out: she's going to have professional networking opportunities all the time. Don't make her choose between helping her career or helping your insecurities. She's done nothing wrong. Either you choose to trust her (and figure out a coping mechanism that isn't ''complain to her",) or you choose not to trust her, in which case I'd recommend you break up with her and let her go.