Altere este bloco do código:
echo "DUMPING TABLE: $t"
mysqldump -h $DB_host -u $DB_user -p$DB_pass $DB $t > $DIR/$t.sql
(( tbl_count++ ))
Para isso:
echo "DUMPING TABLE: $t"
if [ -e "$DIR/$t.sql" ]; then
echo "TABLE $DIR/$t.sql exists, skipping..."
else
mysqldump -h $DB_host -u $DB_user -p$DB_pass $DB $t > $DIR/$t.sql
fi
(( tbl_count++ ))