Order from DeseretBooks.com and charge to ward?

I have been asked by my Bishop to order 5 copies of The Miracle of Forgiveness. Books like this are not available via store.lds.org. Is it possible to order books online from Deseret Books and charge them directly to the ward? Or should I just pay for them myself and then get reimbursed?

You will have to pay for them and then get a reimbursement.

Back in April 2018, our bishop wanted to buy a copy of the booklet "Oh how we need each other" for each sister in our ward. Our executive secretary went to Utah to visit family, and while he was there, he ordered over 150 copies of the booklet from Deseret Books, and charged the order to our ward. We received an IROP for the order. I don't know the details of how he placed the order, but it is possible to bill the ward.

Yes, I believe it is possible to do in person (in Utah at least most Deseret Books and Distribution Centers are integrated). It might be possible to make an order over the phone and charge it to the ward if they take phone orders (from their web site I couldn't tell if they do or not). But I don't think there is any way to make an online order and charge it to the ward.