Is the Bible against having a woman as a US President, CEO or other positions of authority over men.

Great question! I do not see the New Testament giving any instruction directly to the government or corporations / businesses. The focus of New Testament exhortation is the church.

Romans 13, for example, describes the government's role, but to inform the church regarding submission. It is not giving instruction to the government.

The prohibition of women in authority over men is clearly given in the context of the church (1Timothy 2:12-14).