If I understand correctly, you want the minimum distance (along with the stop_reference) for each service_id. If you didn't need the stop_reference, you could just do a GROUP BY:

-- not what you want
SELECT service_id, min(distance) FROM table
GROUP BY service_id;
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But then you lose the stop_reference information, because you've "grouped" that away.

So what I'd probably do is use ORDER BY:

SELECT stop_reference, service_id, distance FROM table
ORDER BY service_id, distance;
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Then you just print out (or store) every time the service_id changes:

my $last_service_id = -8675309;    # for a good time, call
while ($sth->fetch()) {
    if ($service != $last_service_id) {
        print "min dist for service '$service' = '$distance' at stop '
+$stops'\n";
        $last_service_id = $service;
    }
}
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