What is the function of a gallbladder and is it related to my bladder?

No. The gallbladder is involved with the digestion of fatty foods. The urinary bladder holds urine that has been filtered from the kidneys. The two structures are unrelated.
Stores bile. The gallbladder stores and concentrates bile that is made in the liver. It also secretes some mucus from its internal lining. The gallbladder responds to fats entering the duodenum by squeezing bile out into the dodenum to emulsify the fats and aid in their digestion and absorption. It has no association with the urinary bladder.
No. The gall bladder stores and concentrates bile made by the liver. Bile is needed as a detergent to digest fats in our diet. The urinary bladder is a separate system and has little or no bearing on the function of the gallbladder.