bnme is variable that stores selection set - not block name...
Even more, if you supply correct filter '((0 . "INSERT")) - you have to extract bnme from it - iterate or something else (INSERT type can also be xref, not only block, so pay attention to that too)...
(tblsearch) approach is good, but like I said, supply correct argument to it - bnme that is string with desired reference block name...
(= bnme (tblsearch "BLOCK" bnme)) is not needed that way - (tblsearch) returns not block name, but table list with block definition dxf basic data...
Only this is enough :
(if (tblsearch "BLOCK" bnme)
... then
... else
)