I assume you mean currant? (At least that's what we call them over here) I would try looking at examples of grape bonsai, which they bear some similarities to. They are kind of like a straight-growing grape vine

They have large lobed leaves that are difficult to reduce, as well long straight growth, so I think you would have to struggle to keep the growth restrained and to develop an interesting trunk. However the flowers and berries would look nice

I've seen some interesting bonsai over the years with woody shrubs that I never thought could be trained, so I don't see why you couldn't try. By the way do you know what kind of currant? They tend to either be black, red, or white (based on the color of their berries).