Why not start a company called the United States Federal Bureau of Fugitive Enforcement ?
You could give yourself the title of Supreme Chief Agent in Charge
Seriously, I'm not picking on anyone but just pointing out what some idiots have done in the past.
If your a licensed Bondsman / Bail Agent then why not use that as your title ?
If your state has a licensing requirement for fugitive recovery then use the title the state gives you, ie: Bail Enforcement Agent in NY & CT.
If your not a Bondsman and just do recovery / investigations for Bail Bond Companies then the title "Bail Investigator" might be good.
I used to conduct investigations on prospective clients for certain bonding companies to determine what kind of flight risk they might be, so I did more than just recovery work.
Assisting with underwriting risk can be a valuable service, for instance one of my clients was determined to start writing immigration bonds, I talked him out of it by telling him of my experience chasing immigration skips and he thanked me after seeing some of his competitors go under because of skips from immigration bonds, after that he began paying me $50 a head to conduct a preliminary investigation on many of his prospective clients, it was steady work until he retired and sold the business to someone who cut corners and went under.
I think the only acceptable titles in Ohio are Bail Agent or Private Investigator depending on which license you hold, if your a licensed PI and do work for Bail Bond Companies then using the term Bail Investigator should be ok, as long as your not using prohibited titles or holding yourself out as an "official" of some sort you should be fine.