Does your cultivar have a name? One of the more popular is Round of Nice/ Tonda di Nizza which is a large bush. It will sprawl as much as 6 feet under good conditions.
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Most all Summer Squash are Bush type. Winter Squash are mostly vining. The few summer vine exceptions that I can think of off the top of my head are listed below.

Zucchetta rampicante 'Tromboncino'
(www.superseeds.com)
This is the vining zuchini. As far as I know there are no vining yellow squash, pattypan squash or round zuchini. They are all Bush.

There are also the cucuzzi (rareseeds.com), which are an edible gourd. They are light green, elongated and are eaten like zuchini.

Also the tatume (victoryseeds.com) are round light green summer squash, that grow on a vine.

Territorial seeds has a vining zuke called Black Hawk.

Hope that helps!
Susan