The term blue blood came to be associated with the aristrocracy simply because it was not uncommon in earlier times for European nobility to have skin that appeared to have a blue cast. The bluish (or sometimes greenish) discoloration of their skin was often caused by a condition known as Argyria.
Argyria it the result of ingested silver particles that are not able to pass through the body being deposited under the skin. Historically this was caused by particles from silver eating utensils being swallowed along with food or silver being taken for medicinal purposes. Since aristocrats were the ones who could afford medicine and who enjoyed the daily privilege of eating off of silver plates, dranking from silver vessels and as the saying goes being born with "a silver spoon in their mouth" it was a condition that was more common among the upper class.
During this same period in history having pale skin "untouched by the sun" was a mark of status among the wealthy who did not have to labor outdoors. Argryia would have certainly been more noticeable among individuals with untanned skin however it is also thought that the term may have come about simply because veins were more noticable among those with pale complexions even if they weren't plagued by this condition.
Argryia is not often seen today however it did become newsworthy in 2002 when Stan Jones of Montana ran for the U.S. Senate. Mr. Jones who out of fears that the Y2K bug would render the world helpless and without antibiotics begin a heavy regiment of colloidal silver which permanently turned his skin blue.