First off, hiding a snake from your mother is not a good Idea... I'm 19 and speak from personal experience. please don't do that.
There are some simple facts that will help your argument, but in the end if she says no it really is an all parties (including the snakes) best interests for you to just wait until you are out on your own.
A BP has never killed a human, not even a baby.
Bp's stay small 3-6 feet, and most stay in the 3-5 range.
easy to care for, make no noise and very little to no smell (their poop does smell of course, but that should be cleaned up before it becomes an issue)
They don't get hair all over the house
If she doesn't want to see it, they hide most of the day and are only really out at night so that shouldn't be an issue.
My best advise it to get her to hold one. going to a reptile show with her will very likely get her on your side... but as I said before don't try going behind her back. You won't be able to take proper care of the BP and that simply is not fair to the snake.
I will just say this now to get it out of the way, avoid pet stores at all costs. Their reptiles are in poor health, their products are very overpriced (and usually subpar) and worst off their employees 9 times out of 10 simply do not know anything about reptiles so the information that they give out is poor at best and leads a lot of people to this site with a BP in very bad shape.