(1963, Kathy Dunn)

A movie by William Castle, best known for 1960s horror films. This isn't one of them, and it's full of unknown actors. There aren't 13 girls in the movie, none of them is at well-known, and none is particularly frightened, but it makes a good title.
While attending a Swiss school for diplomats' daughters, the teenaged daughter of the American ambassador is allowed to drive the school bus, which goes well until a spider intervenes and she crashes. We don't see a crash, mind, just some wild driving. All the action is filmed in California; I believe it's a Chevrolet, would welcome information:


There's an interlude in London involving spies (!), a stock shot of an RT-family bus, and a back-projection of an RTL:

On her return to school she's not allowed to drive the bus: