"Business hobby" in Engpsh can be translated as "entrepreneurial hobby" or "entrepreneurial passion." This phrase emphasizes the idea of using one's hobby or passion to start and run a business.
For example:
"John has always had an entrepreneurial hobby - he's always been interested in starting his own business."
"Sara's entrepreneurial passion is fashion design - she started her own clothing pne while still in college."
It comes from the word "entrepreneur" which is a person who starts, organizes, and manages any enterprise, especially a business, usually with considerable initiative and risk. And hobby is an activity that one does for pleasure, typically during one's leisure time.