This method is not documented. I assume it is simply a convenience method for setting the index.

Object put(int key, Object v)

Why would someone use a string value to specify the index? This is obviously here to support the interface. You may want to specify this in the JavaDocs (i.e., use the int).

Object put(String key, Object v)
Put a value at an index.

Perhaps the example at the top of the class should also include:

BasicDBList list = new BasicDBList();
while (something) {
list.add(new BasicDBObject("foo", "bar"));
}

myObj.put("list", list);