Welcome "Is This It'!
Check out the post here. It has a good discussion of what the Bible Really Teaches in regards to the use of Blood.
That post has well-reasoned, scripturally supported lines of reasoning. Here's my executive summary of the life vs. blood connection: Israelites could not eat blood from an animal whose life they took. They had to pour out the blood on the ground as atonment (to pay back for) the life they took. If an Israelite found an unbled animal already dead, he could eat it and be unclean for a day, or sell it to a foreigner to eat. The command to 'abstain from blood, and from things sacrificed to idols' given in the 1st C. was to promote peace between the Jews and Gentiles who had an issue over circumcision. The command to 'abstain from blood' must be understood in the context that the Jews understood the law. On this point alone we can see why there is no problem with accepting a blood transfusion: No life was lost to provide the blood for the transfusion, therefore it is not necessary to pour out the blood in atonement.
There's also a really good post on freeminds that is very detailed and addresses the context under which 1st C. Christians refused to drink blood.