Doris Day carries a white wicker bucket bag in The Man Who Knew Too Much (1956) the suspense thriller film directed by Alfred Hitchcock, starring James Stewart and Doris Day. The top handled bucket bag is made of wicker/rattan with metal fittings and is painted white with red lining.
The bag co-ordinates with her blue 50's style summer dress with white belt and it comes in handy when Jimmy Stewart's character needs to write down a message in a crucial scene early in the movie.
I see some vintage wicker basket purses on eBay this week that are very like the one in the film. Here is an example: Vintage Asian Basket Purse Metal Swing Latch Closure 7.5" x 11" There are another one or two like it listed on eBay as well - as a craft project a shabby one could be painted white and lined with red fabric to look like Doris Day's handbag in the movie as an authentic retro / 50's style accessory.