Japanese garden design is strongly connected to spirituality. Shinto, Buddhism and Taoism are often the source in the creation of different garden styles. They are intended to be places of peace for meditation and spiritual contemplation and prayer.
While bridges have become path ways linking garden visitors from one part of the garden to another, bridges do have spiritual meaning in Japanese gardens. Some bridges symbolize the path to paradise and immortality. The famous Kyoto garden bridge, Byōdō-in, connects the Phoenix pavilion with a small island of stones, representing the Mount Penglai or Mount Horai, the island home of the Eight Immortals of Daoist teaching.
Other special islands in the Zen Buddhist tradition, such as the crane and tortoise islands, are sacred and not accessible by bridge. If one sees a bridge to an island in this type of garden pond, these are ordinary islands called nakajima (since they are accessible to the public). See KotoJazz 9: Island of Japanese Gardens for more information.
Bridges can also simply serve as functional links between different eco-regions or sections of the Japanese garden. Stone bridges are called ishibashi. Wooden bridges are dobashi. Arched bridges are known as soribashi and flat bridges are hirabashi. While most bridges are not colored, the red painted temple bridges come from China.
Here are some interesting links to information about Japanese garden and bridges: