[Okay, that's quite a good sign, he looks genuinely concerned and sincere. But then, she's wary of anyone trying to get into Bucky's life since he came back. There had only ever been one other sort of boyfriend and he had been a total disaster, it makes her concerned that Steve might be another Brock Rumlow in disguise.]

He's fine, and a bagel sounds good.

[Actually, Bucky will probably kill her when he finds out she's come to do this, but she'll take it as worth it if she can protect him.]

I just want to make sure you're good enough to take him out on a date, you can pretend I'm the equivalent of a Dad with a shotgun when his little girl goes to prom, if you want.