I spoke to son the next day. He asked me if I was dating someone and said, "Dad, I just want you to be happy." I told him that for now, my private time is my own, and I asked him to respect that. I also have asked him to come to me directly if he has issues he wants to talk about.
I am curious on why you didn't tell him the truth? Seems to me like a teachable moment to set an example "son I am currently still married to your mother and not interested in dating anyone".
Think you may be reading way to much into her interest. She just wants you to be doing the same as her so she isn't painted as the bad guy.