Hi the doctor thinks my mother has leukemia but because my mother does not want the bone marrow test because of her age 88yrs what can my family expect to see in the way of her health what kind of signs if she has it

It is impossible to say because there are many kinds of leukemia and you don't even know if she has it. And all the leukemias are part of an even broader group of blood disorders.
(I would have made the same choice not to have the tests were I her age.)
But in general you might see fatigue and easy bruising and infections. These are common by age 88 anyway. So keep her walking area safe from sharp furniture and scatter rugs, hope she will eat fresh vegetables and get enough fluids, watch her skin, and look for signs of cold symptoms. You don't need to rush to the doctor when you see bruising, but do watch out for breaks in the skin or tiny weeping spots. Get some bottles of saline (salt water) and gauze for any such breaks, or sign up for visiting nurses to do it.
Death can be from pneumonia, organ failure, or other causes, even ones she might have aside from what's going on with her blood cells. There's no way to predict.
Try to shake off the possible diagnosis. Try not to see this as a sudden change or a death sentence, or a need to flutter around in a panic. Given the fact that she doesn't want the test, it sounds like she just wants to have her usual life while she can, and her family around her.