I am not sure why you put the table name and column names in single quote.
Try:
"SELECT * FROM tbl_permits WHERE tbl_permits.bid='" & txtSearch.Text & "' OR tbl_permits.company='" & txtSearch.Text & "'"
You were missing the single quotes around the searchtext values passed to query.
Further, I would suggest you to use 'parametrized query'. It will overcome lots of issues and is much cleaner and safer way to execute queries.
UPDATE: You should use
parameterized query[
^] with your command.