Вам необходимо указать имя класса, так как это не BillingAddress или ShippingAddress.
class Order < ActiveRecord::Base
# foreign key not required here because it will look for
# association_name_id, e.g. billing_address_id, shipping_address_id
belongs_to :billing_address, :class_name => "Address"
belongs_to :shipping_address, :class_name => "Address"
end
Для завершения ассоциации:
class Address < ActiveRecord::Base
# foreign key required here because it will look for class_name_id,
# e.g. address_id
has_many :billing_orders, :class_name => "Order",
:foreign_key => "billing_address_id"
has_many :shipping_orders, :class_name => "Order",
:foreign_key => "shipping_address_id"
end