Not every verb requires a prefix. In the case of pergi it never takes a ber- or meng- prefix. It's just always on its own. The only derived forms that KBBI mentions are nouns kepergian (departure) and bepergian (travel)
No, "pergi bersama" doesn't mean "dating". There aren't many verbs with double meaning in Indonesian. "I'm dating him" is "aku berpacaran dengannya", though in casual speech it can be "aku pacaran sama/dengan dia".