Problem, there's no method:
bool ChangePassword(string newPassword);
You have to know the current password (which is probably hashed and forgotten).
This is an easy one that I wasted too much time on. Hopefully this post saves someone else the pain of slapping their forehead as hard as I did.
Solution, reset the password randomly and pass that into the change method.
MembershipUser u = Membership.GetUser();
u.ChangePassword(u.ResetPassword(), "myAwesomePassword");