I have a bat

I have a bat in the house.  How it got here I haven't a clue.  It presented itself night before last as I was eating dinner.  The only reason I know it's here is that I saw it.  They make no noise when they fly unless you are very close and hear the almost silent flutter.  I opened the front door hoping it would fly out but no success.  Unfortunately my tripod cat got out without me knowing it so she spent the night out on the front porch.  I never saw her get out.  When she didn't come running when I doled out treats I knew something was off.  When I went out on the porch and rattled the treat container I heard her small meow come from under the grill cover.  Poor baby, she didn't know what to do, so I picked her up and brought her back into the house.  I don't think she'll do that again.  Last night the bat appeared again, flying around trying to find a way out.  I opened the east facing window, and took off the screen, left the window open hoping it would find it's way out in the moonlight.  Sigh, I don't think so.  I finally fell asleep with soft whirring sounds as it flew around the room.  Actually I won't know until tonight.  I'll keep the window open again if I hear/see it but won't be able to when we get rain.
A few years back, as I was putting on my waders, I felt something quite uncomfortable in the right boot.  When I took them off I discovered a small dead bat in it.  Now how it got there is anyone's guess.  I leave the waders hanging on a hook on a 6x6 post in the basement.  How the heck did it get in the house, never mind inside the boot of my waders?  I can only wonder.  As to the present guest I can only wonder there also.  All windows have screens and are closed as are all the doors.  The dampers in the chimneys are closed as well.  I rarely open the front door at night, except to let in the cat.  One of those things called damned if I know I guess.  I really hope the guest will find it's way out tonight if it didn't last night.  There's nothing for it to eat. I don't want to find a dead bat anywhere in the house.
Any suggestions out there?
Y'all have a loverly day and remember:  normal is just a setting on the dryer.