"It's okay," really, there was nothing for Elsa to apologise for. Emma had just inserted herself into Elsa's day with pleas for some assistance, so it wasn't a far reach for the sheriff to wait if the queen got caught up in other things. "I wasn't waiting long." There was no reason to make her feel bad about Emma's insistence.
Strangely enough, considering how adamant she'd been about getting the assistance right then and learning this now, Emma wasn't entirely sure where to start, what to start with or how to ask. It seemed fairly personal, really. Asking about magical abilities and what not, like asking what parents did for a living when you were in middle school just to find out who had the most money (and it was never Emma obviously). Still, she'd dragged Elsa out here, and she was eager to figure whatever she could out. She just had to jump in with both feet and exercise some of that family tact.
"So, I take it your magic is emotional, like mine?" It was probably fairly unfortunate for them that way, since Emma's emotional stability of late was highly questionable. But that was all the more reason to figure this all out.