Excellent olive bonsai subjects can be made from Olea Europa, also known as the Mediterranean Olive. In the United States, good examples are most often found in California. The climate there is much like that of the native climate for this tree.
If your bonsai olive was begun from a young plant, seed or a small cutting, it's unlikely you will have a masterpiece such as this in your lifetime.
(It will still take many years.) Meantime you can be working on other bonsai trees. There's a saying in the bonsai world … “If you want a big bonsai, buy a big bonsai.” You don't have to pay thousands of dollars for the perfect tree, purchase a pre-bonsai that someone else has given a head start.
Nebari such as this is only one of the many attributes of olive trees. It also has small leaves and small fruit. The fruit takes many years to develop on young trees. However, air layers from old trees will bear fruit more quickly.
This tree is easy to care for. Basically, it likes lots of sun and fast draining soil.
Trim frequently to keep the shape. It doesn't mind being a little root bound, so you most likely will not need to repot annually.
Although it may survive indoors, the leaves will become larger and it will not thrive as well as outdoors in the sun. A frost is unlikely to kill the tree, but it could damage the leaves. Protect from freezes.
The Bucida species, commonly known as “Black olives” are not olives at all. They look nothing like the European Olive. They are tropical trees and they have very different needs. However, they also make excellent bonsai subjects.