It's a simple acid-base-reaction. In order for bile to do its job, i.e work as an emulsifier, it needs to in a basic environment. Bile acids are therefore in their charged, negative state.
The reaction of HCl with bile acid would then be.
[BILE]-COO- \+ HCl --> BILE-COOH + Cl-
In the human body the reaction would be:
[BILE]-COO- \+ H3O+ \--> BILE-COOH + H2O
There will be hardly any free HCl in the human body, it will immediately react with water to form H3O+ and Cl-. H3O+ will then react with ionized bile acid to give the neutral form of bile acid and water.
So, depending on how you look at it, the product is neutral bile acid and (water or chloride).