The optimization process and recommendations:

1. Avoid Subqueries (query line: 6): We advise against using subqueries as they are not optimized well by the optimizer. Therefore, it's recommended to join a newly created temporary table that holds the data, which also includes the relevant search index.
2. Create Optimal Indexes (modified query below): The recommended indexes are an integral part of this optimization effort and should be created before testing the execution duration of the optimized query.
3. Replace In Subquery With Correlated Exists (modified query below): In many cases, an EXISTS subquery with a correlated condition will perform better than a non correlated IN subquery.

Optimal indexes for this query:

ALTER TABLE `operation_proportions` ADD INDEX `operation_proporti_idx_operator_route` (`operator`,`route`);

The optimized query:

SELECT
        routes.route_number,
        routes.frequency 
    FROM
        routes,
        (SELECT
            operation_proportions.proportion 
        FROM
            operation_proportions 
        WHERE
            operation_proportions.operator = 'Venture Travel') AS Prop 
    WHERE
        EXISTS (
            SELECT
                1 
            FROM
                operation_proportions 
            WHERE
                (
                    operation_proportions.operator = 'Venture Travel'
                ) 
                AND (
                    routes.route_number = operation_proportions.route
                )
        )