@rdangel07: -If you want to disable the header section then you can follow this steps
Go to=> Appearance=> Customize=> Theme Options=> Header Options=> Check to disable the header options(which will also disable search options in header section)
-If you want to hide the search option from the header section without disabling the header top part, then you can add this css
Go to=> Appearance=> Customize=> Additional CSS=> add the following css code
#header-search {
display: none;
}
Let me know if this helps you out!
Kind Regards,
Sapana