We've had the same type of situation happen although we never made it to actual visits. My 14 yo ds's biological father has called us a few times in the past wanting to set up visitation (usually when the child support people catch up with him). He has seen his son three times in his life, all of them when he was under 2. Last I heard, he didn't live in our state but he moves a lot.
As I don't know anything about his father, what his lifestyle is like, etc, I was not willing to allow unsupervised right off the bat. As his biological father didn't want me involved in any way, I set it up for the initial meeting to be at a counselor's office. Our plan was that the counselor would oversee 2 hour meetings for 4 times or so and then, depending on what ds wanted and what the counselor saw in those meetings, we would allow trips to restaurants, etc. This was when my ds was 12. I devised this plan after biological father called a couple of times really wanting to meet ds. Unfortunately, after those two calls, he never would call back and didn't respond to emails.
That was my plan as I really didn't feel comfortable just sending my son off with some stranger, even though he is his biological father. Of course, a big part that played into it was that biological father had been abusive and a drug user when I knew him so YMMV.