According to nLab:

> If \\(\mathcal{C}\\) is a 2-category, there is its double category of squares \\(\mathrm{Sq}(\mathcal{C})\\) whose objects are those of \\(\mathcal{C}\\), both of whose types of morphisms are the morphisms in \\(\mathcal{C}\\), and whose squares are 2-morphisms in \\(\mathcal{C}\\) with their source and target both decomposed as a composite of two morphisms. (These squares are sometimes called *quintets* \\((\alpha,f,g,h,k)\\) where \\(\alpha\colon f g \to h k\\), and so this double category is said to be a quintet construction.)

so it sounds like any bicategory is a special case of a double category.