As per the terms of the 12th amendment a person seeking the office of Vice President must be eligible to be president. As per the terms of the 22nd amendment no person shall be eligible to be president more than for two terms.

Bill is not eligible to be President, or Vice President, and if he'd end up in some other office in the line of succession, he'd be ineligible should he end up first in line he'd be skipped over. For example if he'd be the Secretary of State, and President, Vice President, Speaker of the House, and President Pro Tempore of the Senate are all dead, then Secretary of Treasury would be next in line since Bill is ineligible.