Taking her from the bus stop could give you a lot of time too.
I agree that someone that only wanted Jayme could have decided to go in at night to give themselves more get away time or more cover. I could even see that someone decided to murder both parents to take her.
I can't see deciding to face an armed father. That's a huge risk.
Taking her from the bus stop allows an absolute max of about 2 hours for a getaway, and probably less than that. That's assuming nobody sees you doing it, which would be difficult in and of itself. As soon as she is marked absent from class, it would be reported to the school office, and the office would call the parents.
Taking her at night and killing the parents buys you a minimum of 10 hours, and possibly a lot more than that. The school would call the parents, but they obviously wouldn't answer because they'd be dead. Eventually someone would realize that no one had heard from anyone in the family that day so they would go to check on them. But by the time someone actually goes to the house it might be lunchtime on Monday, or maybe later that evening.
I also don't think the perp would assume the dad would come to the door with a gun. Most people don't. And maybe they knew enough about him to know that he didn't carry one on him. While he likely had guns in the house, most people with kids will keep them in a safe, or at least put away somewhere where the kid can't get to it easily.
Sounds like all of the family guns were accounted for, so it could have been as simple as knocking on the door to draw him to the door unarmed and then starting a blitz attack. He'd have no reason to go get his gun out of it's hiding place just to see who was at the door.