I'm so happy you and the baby are ok!
So sorry for the bat incident.
Only thing that I can assure you of is the bat was just as scared as you guys were.
They're blind and entering a daylight / inhabited / artificial light area can really confuse them. They'll try to find their way out but in the same time their instincts tell them to go for the patches of heat they "see" on their thermo-sensor map...not sure if that makes sense.
I have had bat incidents, but usually I found them in broad daylight completely stunned. I took them off with a blanket and deposited them under some shed.
The ones I have met shriek horribly, do not bite but can scratch and put up quite a fight when you restrain them.
The hardest part is catching them; I was using a blanket or a coat and throwing it on them.
I know the bat probably seemed like the imprsonation of vice and murder, but please don't kill it if possible
They're harmless usually and they also eat a lot of pesky bugs.
Edit: And they're incredibly ugly at face. Oh boy.