In my experience, the biggest source of rumors and conflict regarding workplace romances comes from the fact that no one (except the two individuals involved) can tell if the relationship is honest or not. I've never been quite in your exact situation as a C level, but I am married to someone whom I met while in a director role at a prior employer - we started dating when she was in a junior management role and about to be promoted to a director position. I left the company shortly after. The start of our relationship, her promotion, and my departure were all pretty close together. So I got a little bit of the flavor of "so-and-so is dating someone in upper management and one of the involved parties has left" that you're feeling.
When I say "honest," I mean it in the sense of workplace legitimacy - are the two people in the relationship able to function appropriately in their jobs, despite the personal connection? Or, are they using the personal relationship and/or workplace power dynamic for some sort of illicit personal gain?
And because no one really knows this except the people involved, there will be plenty of people who will either make up or at least hint at the worst case scenario especially if you give them reason to, and then the gossip train leaves the station and things get ugly.
Really, I think there are only a few responses to this threat:
- Don't get involved in workplace romances. Some people consider this the only option. Good for them, if they can pull it off. Personally, I think it's a terribly limiting option, and unrealistic anyways. But that may be personal bias, speaking as someone who's married to a prior coworker.
- Hide the relationship. Difficult - maybe impossible, at least very risky - to actually pull off. Plus, it gives a bad perception if/when people do find out. Even having a "cool down period" before making the relationship more official feels like it verges on hiding things to me, but that may be a gray area I suppose. And at any rate - if the relationship develops and becomes long term, it's likely to be literally impossible to permanently hide it from coworkers - they're going to find out eventually. Trying to hide it means they're going to find out in a way that paints you in a bad light. Better to let them find out in a way that doesn't give a bad impression. Which leads to,
- Don't hide it. Don't give people anything to talk about. If your relationship is legitimate, you really have nothing to hide. You won't eliminate rumors, but you can at least reduce them, and preemptively set yourself up to defend against any that may be damaging.
Of course, that third point can be easier said than done. In the practical sense, especially if there is a leadership/subordinate relationship involved, it can be difficult. For my wife and I, we tried to actively take specific steps related to the workplace aspect of our relationship. These steps were not only to allow us to be honest with ourselves that we weren't hiding anything, but also to give us the capability to show or prove that we weren't, if it was ever challenged.
- When we were interacting one on one in the workplace about day to day workplace topics, we made sure there was some sort of basic paper trail, i.e. an appointment in our outlook calendars listing a subject for the meeting. This was done as a basic cover in case there was ever any question about if we were chatting about our weekend plans for two hours on Friday - when we were really focusing on the proposal for That Big New Client or whatever.
- When we had any level of official, important interaction that may even hint at favoritism, we made sure there was a paper trail or process that was either in someone else's hands, generated by someone else, or validated by someone else. For instance, part of my role was churning data from our core system to generate numbers that were used for performance metrics (quality control, throughput, etc). I made sure someone on my team besides just myself understood that process and was involved in coding the queries used, just as a fail-safe from people trying to claim that I was padding her numbers because we were sleeping together or anything like that.
- When we first reached the point of entering into a meaningful relationship, we made sure we understood and followed company policy. It turned out that our employer basically did not have a policy that applied to our relationship (which we were a little surprised by), but we made sure to find out. And, as an additional measure, I disclosed the relationship to my boss anyways, as an insurance against him "finding out" via some untrue rumor. He and I had a great personal friendship and a good workplace relationship, so it was natural to tell him, anyways.
A lot of this advice may be "water under the bridge" for you, as she doesn't work for your employer any more, but I think at least some of it will meaningfully translate to your situation. At least, the "don't hide things" part. For instance, you mention industry events that include an invite for a spouse or partner. My advice: go ahead and bring her. If you're dating, it's likely people will know you're dating. And if people know, and you show up at the Big Industry Dinner without her, people will assume you're trying to hide the relationship. You don't want that.
My wife still works for the employer we met at, and through the early phases of our relationship (after I'd left that employer but before we were married), I went to a handful of company/industry events with her. People were glad to see me there, and it was no big deal. We took the steam out of any rumors. Meanwhile, a mutual coworker friend of ours, who had also started dating someone from the workplace who'd left in similar timing to me, chose not to bring her to those events. You can guess which couple was the focus of the rumor mill. In fact, that other couple had a pattern early on of taking steps to try to hide their relationship, despite it being completely legitimate, and I can absolutely tell you it went very poorly and was a huge cause of tension and stress for them.