I am an undergraduate student of biology

Maybe not what you want to hear, but I would (no offense) not even consider hiring someone without a degree and probably little or no professional experience for a paid job in bioinformatics. It's after all a field that requires a fair amount of knowledge and experience to make sure things are done well. As a student you gain experience along the way so doing mistakes in your own project is fine, but for a paid freelander one expects corrects (that is not flawed in a technical sense) results. Can you guarantee that?

Why not a normal student job? I administrated the website and helped organizing events at one of our institutes during my bachelor's to get some cash in.

I agree with the other comment. I would also note that most people I know in this field have at least an MSc if not also a PhD in a relevant field. You aren't exposed to much bioinformatics outside of dedicated BSc courses, and even then I would be skeptical.

That said, there are plenty of things you can do to help on your way into a bioinformatics career. Start using the more common languages (e.g., Python and R), play with public datasets (e.g., on NCBI), use workflow and environment managers (e.g., Nextflow and Conda), and crucially provide a few examples of your work on github.