Liver biopsy is usually a day surgery kind of thing. I've done post-procedure care and, yes, you're right about the patient needing to take precautions to prevent bleeding - usually several hours laying on their back with a pressure dressing on the biopsy site.
Also, it sounds like there is a high probability of a blood clotting disorder at work based on what you've described here. The WTS has approved the use of clotting factors for JWs for a very long time. I've administered Antihemophilic Factor/von Willebrand Factor concentrate (which is derived from "large pools" of donor blood and fractionated) to a JW patient without one peep of protest once I inform them that they are receiving a blood product.