Use EXPLAIN to see the execution plan.
Lacking any information about the table, we're really just guessing.
I'd try achieving the specified result like this:
CREATE INDEX `mt_ex_15_IX1` ON `mt_ex_15` (`itype`,`s`,`bdate`);
SELECT t.s
, SUM(t.bdate > '2014-10-01' AND t.bdate < '2014-11-01') AS `total`
FROM `mt_ex_15` t
WHERE t.itype = '3'
GROUP BY t.s
HAVING `total` > 0
ORDER BY t.s DESC
Comparing the EXPLAIN output from this and from the original will (likely) show that the two queries are using different execution plans.
FOLLOWUP
With a suitable index, MySQL can avoid an expensive "Using filesort" operation. The index I recommended above will render the index on just the itype column redundant, and that index could be dropped. (Any query that was making use of that index can make use of the new index, since itype is the leading column.
The recommendation for the new index is based on the query... an equality predicate on itype (make that column the leading column), followed by s since there's a GROUP BY on that column. Including the bdate column in the index means that the query can be satisfied from the index, without a lookup to the underlying data page.
We'd expect the EXPLAIN output "Extra" column to show "Using index", and not show "Using filesort".
If adding an index is out of the question, then your best shot at avoiding a "Using filesort" is going to be to make use of an existing index that has column s as the leading column. But that means that the query is going to need to examine every row in the table; if the columns bdate and itype aren't included in the index, then that means an index lookup to every row in the table. But, this may perform faster. Check the output from EXPLAIN for this query:
EXPLAIN
SELECT t.s
, SUM(t.itype = '3' AND t.bdate > '2014-10-01' AND t.bdate < '2014-11-01')
AS `total`
FROM `mt_ex_15` t
GROUP BY t.s
HAVING `total` > 0
ORDER BY t.s DESC
index(bdate,itype,s).Is your bdate date or datetime?s? How many distinct values forsare there? Since you are sorting on calculated value, if you have large number of distinct values fors, the sort may still take some time.