I believe it just depends on the context. If your friend were talking about their mother and you wanted to bring up yours, I think "私のお母さん" would be the better choice. If it's obvious from the context that you would be talking about your mother, I believe "お母さん" would sound more natural, as the "私の" might come off as redundant.
You may want to wait for a native speaker to answer though. This is just an educated guess based on what I've learned so far.
EDIT: Just as I posted, someone else answered. Disregard this!