Actually, I am not asking about a different means of enforcing the law, but about an entire society of people like Bucephalus. Your answer is very helpful; It is good to know a respectable thinker has already given this some thought.
I am talking about a society of zero enforcement, in which any attempt by one or several persons to force an individual to do anything is universally considered agression. I would defend myself and my neighbors against agression, as I think most people would, but as long as law enforcement is considered legitimate and desirable by most people they won't help my neighbor fight off the repo-man.
The difficulty and simplicity of this mental exercise is using a single idea - no enforcement - to change the meaning of many words rather than changing the words. To get from current society to anarchy, I think, it would be sufficient to pass a "law" declaring any and all coercion/enforcement as "criminal" aggression, theft, assault, terrorism... Obviously, "government" cannot even legitimately enforce that "law," so basically we have anarchy but keep the communication value of formal, evolving written statements of how most people expect and desire other "citizens" of a territory to behave.
I guess my own manner of doing business is very similar to how you say Bucephalus practiced law. My business is based on agricultural production contracts: you agree to grow a crop for me, I agree to buy it at a certain price upon harvest, or vice-versa. My business is also based on intellectual property: I am a plant breeder and the use of my varieties is illegal without my permission. I see a lot of value in this system because, in productive activity involving two or more persons over a relatively long period (like a crop season), informal, vague, oral comittments lead to confusion: too often in such cases, my memory of what was agreed or implied wanders in a different direction from my partners' memories. Frustratioon and anger results as someone feels betrayed, making it difficult to continue working together next season.
So I negotiate contracts, we write them together and sign them. That way, at the end of the season we can get them out and remember what was agreed. Useful. HOWEVER, I like to make it clear -- usually written into the contract -- that I WILL NOT PURSUE LEGAL ACTION IN CASE OF DEFAULT ON A CONTRACT OR ILLEGAL USE OF MY INTELLECTUAL PROPERTY.
So the way I do business precludes enforcement from my side. This changes the relationship. Just last week a farmer decided to default and told me "you said I didn't have to pay you." I responded "we made an agreement. As promised, I won't force you to honor it. You do what you feel is right and we will both know what kind of man you are."