In the US, the blood supply is EXTREMELY safe. It's never perfect, nothing ever is, but you're probably more likely to die from complications during surgery than contract hepatitis really.
Ok, maybe that's a little extreme, but it's close.
I had a number of bleeding issues after surgery, a really rough time which was VERY much atypical of most people's experiences here. My wife donated but no one else could because they weren't matches.
I also got a lot of blood from other sources, most of which I just bled back out again.
I was feeling a little "ungrateful" at the time..... =Þ
Actually, I was comatose, again, a rather atypical experience for valve replacement.
As has already been stated here, a lot of patients can donate blood for themselves prior to surgery. It's up to the surgeon or your cardiologist to decide if you can do that, some people with heart problems can't donate because of the stress it puts on their heart. You may also have family members or close friends that can donate for you in advance, tagging the blood ONLY to be used for you if you need it AND for the most part, blood loss is kept to an absolute bare minimum anyways during surgery.
Nothing is truely "bloodless" either but there are a lot of surgical tools used to keep it to a minimum including cauterizing scalpels and other devices which create instant clots as they're used.