You could use ForgotPasswordAgain's initial "won't work" idea as a subquery to grab the full record for the shortest distances.
select a.* from table_name a
join (
select min(distance) as min_dist,
service_id as min_id
from table_name
group by service_id
) b
on (a.distance = min_dist and a.service_id = min_id);
If (service_id, distance) is not a unique key, this will return all the stop_references with the minimal distance. This may be a Good Thing, depending on the application. If you want only one result, adding the appropriate ORDER BY and LIMIT 1 clauses should do the trick.
/is not a guru
//tried it and it worked for me
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