Can a blood transfusion change your blood type?

No.

Red blood cells have a lifetime of about 4 months. So even if you were to transfuse someone with a blood type that is not their own (for example, give type O or type A blood to someone who is blood type AB), their own body would replace these blood cells with the original type within about 4 months.

No, that's impossible. Blood transfusions have to match the donor's blood quite closely to prevent adverse reactions. Also, blood cells never live longer than about 4 months (red blood cells) or a few days (white blood cells), so the transfused blood should have vanished after that time.

Bone marrow transplants, however, can generate blood cells with the same DNA as the donor, however. But for a transplant to be effective, the blood type should be the same.

No. Great care is taken in cross-matching to ensure that the recipient's immune system will not attack the donor blood. In addition to the familiar human blood types (A, B, AB and O) and Rh factor (positive or negative) classifications, other minor red cell antigens are known to play a role in compatibility. These other types can become increasingly important in people who receive many blood transfusions, as their bodies develop increasing resistance to blood from other people via a process of alloimmunization.
The key importance of the Rh group is its role in Hemolytic disease of the fetus and newborn. When an Rh negative mother carries a positive fetus, she can become immunized against the Rh antigen. This usually is not important during that pregnancy, but in the following pregnancies she can develop an immune response to the Rh antigen. The mother's immune system can attack the baby's red cells through the placenta. Mild cases of HDFN can lead to disability but some severe cases are fatal. Rh-D is the most commonly involved red cell antigen in HDFN, but other red cell antigens can also cause the condition. The "positive" or "negative" in heard blood types such as "O positive" is the Rh-D antigen.
HDN prevention started in the 1960s when it was noted children of pregnant women who had received anti Rh immunoglobulin did not develop the disease. From then on, Rh negative pregnant women receive immunoglobulin doses at several moments during pregnancy and after childbirth if the baby is Rh positive. In current practice, Rh negative women of fertile age will not receive a transfusion of Rh positive blood except in desperate situations when nothing else is available.

No.

That would kill you.

The blood transfused in MUST be the same type as what is already in there.

But not only is your BLOOD typed, but so are your internal organs -- which have the same "type" as your blood. This is one of the first things they check when they do an organ transplant. BLOOD TYPES must be the same, too.

IF a blood transfusion changed you blood type, it would damage your internal organs and kill you.

"Not all blood groups are compatible with each other. Mixing incompatible blood groups leads to blood clumping or agglutination, which is dangerous for individuals."

nobelprize.org

So the answer is no.

1) You will not get a transfusion that is not your blood type.
2) If you do it is really bad, but it will not change your blood type.

No, the reason you would get a blood transfusion with the same type of blood than what you have already.