This might go either way...
It may depend on exactly how the process played out. It's possible that you might have an arrest for reckless in the FBI databse which is checked when you get a SIDA badge.
I doubt the NDR shows a reckless, I *think* that's just convictions. But you can and should get a copy of that, also pull your state driving record and your VA record if they allow that. Just to make sure it says what you think it says.
Good news...
1) The conviction was only for a "regular" traffic violation, which is not a PR and liability issue for the company.
2) Unlike the commonwealth of VA, most rational people don't really consider 12 over to be truly "reckless". 85 in a 45, yes but not 12 over.
Best thing is probably to be honest as always, if they ask about CONVICTIONS, you can say no. If they ask about arrests, you should be truthful but explain the situation.
If they ask about arrests and you want to roll the dice, you should maybe talk to an attorney.
IMO if the reckless was issued like a ticket and you were immediately sent on your way that is NOT an arrest. An arrest would require formal booking at the station. Not necessarily handcuffs and a ride in the paddy wagon, but if you went to the station, got finger-printed, processed, and released that would be an arrest.
If you weren't arrested and not convicted of reckless I think you're good. Read the questions the airlines ask and answer them verbatim.
Please not that it's not a crime to lie to an airline. But it is a crime to lie to the federal government, which includes the smurfs. I know a guy who lied to the airlines about a minor conviction, got hired, but then had to fill out the TSA form to get a SIDA badge. He read the fine print on the form that talks about felonies and federal prison...so he wisely decided to list his conviction (probably the only wise thing this guy ever did). Unfortunately for him, the airline staff were the people handing out and collecting the SIDA forms, and they noticed the conviction. He was of course fired that same day.