These are the ages I'm working with:
Sigrid - 18
Bain - 15
Tilda - 12

Also, canonically, Bard is 43 when he kills Smaug, so I figured these ages were reasonable, especially if you go with the common headcanon that his wife died in childbirth. Bard seems to be (at least in the movie) over her death in the way that he can talk about it a little, but it's not a subject that he likes to dwell on or think about (and I mean, who would?).

Bard happened to think that the best part of his day was putting his children to bed.

Not that he got tired of them or wanted them to go away, but he had always liked it because it was something he could always do with them.

He enjoyed tucking them in, even if Bain and Sigrid said they were too old for such things. Now Tilda was getting to the age where she would whine "Daaaa," and get embarrassed when he kissed her on the head, but Bard knew they didn't truly mind. One night, when he had come home late, Bain had admitted that he had a hard time falling asleep without it.

As of late, however, it had become more and more difficult to see them before they went to bed. Meetings with Dáin Ironfoot and long conferences about supplies in Dale took up most of his time, and sometimes he felt too exhausted to even get himself into bed, let alone his children.

Today was a welcome exception.

Bard had become good friends with Thranduil in the time since Smaug, and he figured now was as good a time to have him meet his children officially. They had met him before, in passing, during the Battle of the Five Armies, but he was almost positive Thranduil would not be able to recognize them if he saw them.

Bard wanted to involve Thranduil in "family" events - even if they were as mundane as bedtime.

Bard was a bit nervous. He knew Tilda and Bain would be taken by Thranduil almost immediately. Tilda would love him merely because he was an elf and had pretty hair, and Bain would be interested in his skill with archery. Sigrid might take longer, but Bard knew she would warm up to him. No, Bard was more worried about Thranduil.

Thranduil didn't see to be the kind of person who liked children. After seeing him speak with his own son in such a cold, distant manner, Bard had no idea how Thranduil would interact with someone else's children.

At least he had seemed eager to meet Sigrid, Bain, and Tilda. That had to count for something, right? That had to mean Thranduil would try with them, Bard tried to reassure himself.

And Thranduil had to like his children. If he didn't, how could Bard even consider trying to court him?