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She has a habit of getting all fidgety when she's in front of people.
Literal
She [topic-は] in-front-of-people [to-に] goes-out [when-と] fidgetingly acts habit [subject-が] exists.
Three grammar points work together here. The conditional と marks an automatic, habitual cause-and-effect: whenever she appears before people (人前に出る), the fidgeting follows reliably. もじもじする is a state mimetic (擬態語) for nervous squirming or fidgeting from embarrassment. And ~癖がある frames this as an involuntary habit — 癖 (くせ) often carries a slightly negative connotation, suggesting a tendency that's hard to control, unlike the neutral 習慣 ('habit').