I also changed in the Configuration Report section the csv_columns and excel_columns configurations but still the field bugnotes_count can't be exported.

array (
0 => 'id',
1 => 'project_id',
2 => 'reporter_id',
3 => 'handler_id',
4 => 'status',
5 => 'resolution',
6 => 'bugnotes_count',
7 => 'category_id',
8 => 'date_submitted',
9 => 'last_updated',
10 => 'summary',
)

Same for attachment_count https://www.mantisbt.org/forums/viewtopic.php?f=3&t=23517

there is not a strong reason not to:

commit 7634b19064380b7942107c4f821eb78acc893d06

Author: David Hicks hickseydr@optusnet.com.au

Date:   Mon Oct 5 20:06:23 2009 +1100

Fix #10703: Don't show attachment_count column in CSV output

It is a little complicated to show the attachment_count column in the
CSV output at the moment. Therefore we disable this column from being
usable until such time as someone wants to spend time fixing it up
properly. By disabling the column, we prevent users from enabling what
is currently a broken/non-implemented column.
diff --git a/core/helper_api.php b/core/helper_api.php

--- a/core/helper_api.php

+++ b/core/helper_api.php

@@ -377,10 +377,11 @@
    $t_keys_to_remove = array();

    if( $p_columns_target == COLUMNS_TARGET_CSV_PAGE || $p_columns_target == COLUMNS_TARGET_EXCEL_PAGE ) {
            $t_keys_to_remove[] = 'selection';
            $t_keys_to_remove[] = 'edit';
            $t_keys_to_remove[] = 'bugnotes_count';

$t_keys_to_remove[] = 'attachment_count';

$t_keys_to_remove[] = 'overdue';

}

PR https://github.com/mantisbt/mantisbt/pull/696
partial fix (please read PR notes)

New PR: https://github.com/mantisbt/mantisbt/pull/854