It is permissible to receive blood from the Blood Bank even if the donor was a kaafir. Likewise, it is also permissible to donate blood to non-Muslims as long as they are not fighters of Islam. A fighter of Islam would be defined as one who fights Muslims with weapons or finances such fighting with his wealth, or helps such fighting. If one is not able to know for sure, then it suffices to act according to ghalabat ul-zann (one's best estimate or what is most likely and probable).
ahabbak allaah ul-ladhi ahbabtani fih.
(May Allaah love you as you have loved me for His sake.)