As bacterial DNA cant associate with human DNA, so you need to extract bacterial DNA from the plasma layer of that infected whole blood sample. As that whole blood is infected with that bacteria, so bacterial will be present in the surrounding plasma of that blood.
So, Centrifuge the whole blood at 11,000 g for 8-12 minutes, collect the plasma layer, and extract DNA from that plasma by a column-based DNA extraction kit. Kit for bacterial DNA isolation, moreover same like human DNA extraction kit, just having some different in wash buffer and lysis buffer composition.
There is a company called Molzyme that has kits for obtaining DNA from bacteria in blood samples. The blood cells are first lysed without lysing the bacteria. Then the bacteria cells can be collected for DNA extraction.
I hope you are doing great. Thanks for sharing your confusion.
You don't need to care about the plasma condition ( separated or unseparated whatever). However, it would be best to centrifuge the tubes to not centrifuge immediately after drawing blood. Allow the blood to clot in an upright position for at least 30 minutes but not longer than 1 hour before centrifugation.
Centrifuge for at least 15 minutes at 2200-2500 RPM within one hour of collection and then carefully separate the plasma layer.