How do I know which wire to connect red, black, and white to if the existing is not known since all three wires are black plus bare wire which I anticipate is for the green oven wire.

You will need a volt meter. Set the meter to read at 300 VAC or higher and connect a test lead to the bare wire. You should read 120 VAC between the ground and 2 of the wires and zero between the ground and one of the wires. The hot leads should be Color coded black and red, the other one white. They should be permanently marked with paint -nail polish works well, red for one of the hots, black can be left alone and the neutral should be white. The wires at the panel should be marked the same way. BE CAREFUL, turn the breaker off before painting the leads and VERY careful in the panel.