Hello,
The bitter taste on the skin can be due to more amount of sodium or salts being secreted in the sweat. When the water in the sweat evaporates, it leaves the salts (sodium, chloride and potassium) behind on your skin, which is why your skin tastes salty.If there is any excess of salts then it can give a bitter taste.Excess salty sweat is found in cystic fibrosis.Symptoms are salty tasting or bitter skin, constant coughing or large amounts of mucus and respiarory difficulty.
Did you apply any moisturizer beforehand?This can also cause bitter taste of skin.
In absence of any other factor,I advise you to consult a physician and discuss the possibility of cystic fibrosis with him.
Hope it helps.Take care and pls do keep me posted in case of any additional queries and how you are doing.