Say thanks but no thanks..

Make a good doorstop

I would act confused and wonder aloud how that could possibly help.

I mean, seriously, even if the Bible contained helpful stuff, it's a dogpile of geneology, questionable history, theology, fabulist mythos and outright bullshit. So expecting someone experiencing grief and loss to wade through that to find comfort is really thowing mud at the side of a barn to see if any of it will stick. It makes me question whether the person leading this group is even competent.

I just say thanks and leave it at that. My best man gave me a beautiful bible.It is gold leaf and then in a cedar box. I just looked stunned and had no idea , WTF. I do not want a bible but it was my best man who had recently became a born again. I must add we are no longer even friends as he went down the W bush and Trump path. The bible is somewhere with my ex wife.
Oh the word of god. how it gets going is truly amazing.

How about, "No thank you. I'm an atheist." You'd do the same if someone offered you a Hindu holy book or the Koran.

If you have a fireplace, use it to start your fire.

I have several Bibles in my house. One I keep handy to look things up, if I feel the need. It's one my grandmother gave to my older brother who passed away when he was 18. It has an inscription in her handwriting. I keep it for sentimental reasons. I see it as a historical type book and to look up things to see if it really says I'm being told it says.

Take it, read it, then return asking the really uncomfortable questions that the book legitimately would prompt.

Oh, I've read that book. Not a patch on Agatha Christie.

Or...
You could look the person dead in the eye and say...
"No thank you, I've eaten already. Couldn't eat another bite."
And try to keep a straight face while the look of dumbfoundment washes over them.

I have a collection of religious books, and a bunch of different bibles. If it is one I already have, I would just say,"I have this version, thanks anyways." I don't think people often give people things to be mean.