Your mother is right.
It boils down to knowing the definitions of the words. The definition of bring from dictionary.com is:
to carry, convey, conduct, or cause
(someone or something) to come with,
to, or toward the speaker: Bring the
suitcase to my house. He brought his
brother to my office.
Bringing with involves coming to.
Taking with involves going away from.
When you were talking to your mother, your were going away from her. That is why it was correct to say that you were taking something with you.
If your were talking with your friend over the phone, it would be correct to use bringing, because you were going toward him.
Bringing or taking is relative to the (future, present, or past) presence or absence of a person at the destination to which something shall be, is, or has been brought or taken. This person is not the bringer/taker.
It could be a person to whom the bringer/taker tells what bringing or taking he/she shall do, is doing, or did.
It could also be a person who tells to a third person what bringing or taking the bringer/taker shall do, is doing, or has done.
If the person shall be, is, or was present at the destination while the bringer/taker shall be, is, or was on his/her way, bring is the appropriate word.
If the person shall be, is, or was absent from the destination while the bringer/taker shall be, is, or was on his/her way, take is the appropriate word