If I zap you bitcoins, that's a business
Yes, but this does not imply that the type of property changes. In socialism you can do small businesses with personal property, in that system what is important is your contribution to society and that your actions do not harm the rest of the community (that is why private ownership of the means of production and speculation is not allowed).
So I can sell 3d printed doodads, but not apples at the farmers market?