Can the Board of Directors of a 501(C)(3) organization, change the bylaws to provide for election of Board members by the Board rather than by the membership of the organization?

Probably. It would depend on whether it is allowed by the non-profit corporation statute of the state in which the organization is incorporated. Section 501 (c) (3) of the Internal Revenue Code has very little to do with it.

It all depends what the bylaws say are the rules for amending the bylaws. If the bylaws can be amended by board vote only without membership concurrence, then the board can change the rules as they see fit.