For 'entrepreneur', or even 'businessman', just as in English, there are few words in Latin of such broad meaning. With the senatorial ranks officially forbidden to engage in commerce, it was left to the equestrians, who were content to manage business both for themselves and for others. Within the equestrian order there seem to have been two broad categories of businessman, the negotiator and the mercator, either of which, as 'someone owning their own business,' may answer your requirement; there is a distinction between the two that depends on the circumstances.
While the business of a negotiator was more usually money, the basic business of the mercator was commerce — a trader, wholesaler etc. Both categories included speculators seeking profit through commercial astuteness and, by and large, their activities were conducted outside of Rome. Business was (of course) operated through the all-pervading patron-client system, downwards through all the citizen classes.
The word negotiatores is often equivalent to the 'bankers' (argentarii) or 'lenders at interest' (feneratores) at Rome, but it still included many who speculated in commodities of every kind, from corn and oil to rare materials and works of art. It wasn't used in the Urbs — probably because the senatorials had to avoid the taint of 'merchant' that the word implies.
The mercatores, on the other hand, tended to be contractors (for both labour and commodities — including slaves and wild beasts) or simply traders, shippers and wholesalers. A key distinction is that a notionally independent mercator might be dependent on financial support from (locally) a negotiator in order to manage his affairs.
