Depending on the local laws, that's easier said than done. E.g. in Germany, a private entity (read: person) can't just bill a company. And you can't just write something that resembles an invoice either. Especially, you're not allowed to make it look like a business invoice by putting net sums on it.
A German business on the other side of the transaction rarely will pay anything if there's not a proper invoice (listing net sums and VAT separately) on file. And they usually also require the (business) tax ID of the other party.
To be fair, founding a business is a matter of filling in some form, paying a small fee, and a few days of time (depending on the workload of your local trade office). But still - if this is a one-off thing and you don't even know whether there will be more... I'm not sure I'd want to go through the hassle. Especially if it means having to hire an accountant with monthly costs, when I don't even know whether there will be more income.
