When you get near eligibility the feds will send you a booklet MEDICARE AND YOU. It's massive and tries to spell things out. On pp19-20, there is a chart of Part A covered services. Blood is covered only when you're hospilized, and you pay a little if the hospital has to pay for a private source. It does sound like Part A doesn't pay for the doctor while you're in the hospital. Part B covers lots of stuff, but you have to pay a premium, deducted from your Social Security. Page 39 summarizes what's not covered by parts A and B.
One thing that's been suggested to me...if you travel in a group that offers it (like a cruise or tour) get the health insurance they offer. Why? If you ever have to be transported for medical care in an emergency while on a trip, it could bankrupt you.