A bat visits

I had a bat in the room at 3 am. I heard a fluttering of wings by my
head repeatedly. Thought it was a moth. Eventually I see it, flying
just like in the Abbot and Costello movie with Dracula. I put the cat
in the closet and closed the windows. (All have screens on them.) I
then waited by the open front door as that was the only fresh air
coming in, which is what the bat was going for. In a little while,
the bat came to the front door. It was hard to see but I saw it crawl
around the screen. I opened the door. I wasn't sure but I thought it
flew out. I closed the door and opened the windows again. What an
adventure. How did it get in? From the screen by the kitchen vent?