In both directions we were actually on shared minibus transfers arranged with Wild Horizons. We didn't hire a car, but certainly if you ever want a transfer in that area we'd recommend WH, who were efficient and had good vehicles and drivers.
The bridge is currently being built from Botswana (west of the border crossing in to Zimbabwe) across the river north in to Zambia. There's an old ferry crossing there, which the bridge is replacing, which is notorious for causing truck back-ups for days or weeks.