? you can't filter the blood, of course, as that will remove all the RBCs, which I assume you want. And, assuming it's from a healthy animal, the blood is already sterile/free of bacteria.
BHI is so thick it doesn't filter especially well on its own.
Bottom line: Autoclave the BHI broth to sterilize it (this is recommended anyway), cool it to room temperature, and then add the blood using sterile pipets and aseptic technique. I'd make a big flask of BHI, then add the blood, then aliquot into single-use tubes.