I dont think that you might be able to check your luggage through.
Dont expect too much. BLR is a modern airport, but not fully untilised yet, currently quite some construction going on in the Terminal. Theoretically there is a transit counter, but i mostly see it empty. I would expect it to be quite troublesome to manage to stay airside.
Go to your Hotel, there is not much to do at the Airport.
Yes there is a Day Hotel run by Plaza Premium Landside (Domestic Departure), but I have no idea how you get there without a domestic booking. Its pretty strict in India, no booking no access to the CheckIn hall.