I suffer from arthritis and noted growth on my knuckles for ten years. Doctors aspirated it and blood came out. What is it?

Mucous cyst. Most likely this is a mucous cyst seen often near the last knuckle (dip joint). These occur often in the setting of arthritis. They don't contain blood, but any time you attempt to aspirate anything, you can get blood in return as you go through capillaries.
Uncertain . It could've been dilated vein or a vascular tumor. Or the blood could've come from sticking the needle in there and not related to the growth diagnosis. There can be up to 300 different types of arthritis so importantly what kind do you have? This might help explain the bleeding.