okay i first got a bearded dragon my mom was against then she fell in love with him and plays with him every day haha
now my mom has a HUGE HUGE HUGE!! fear of snakes so when i said i wanted a baby corn snake she was really upset until she saw it then again she said awe its not so bad JUST DONT LET IT ESCAPE!! haha
finally when i wanted a ball python she said if you get it i can't come into your room ever....well i went online with her showed her how gentle they really are and why they are called ball pythons showed her the kind i wanted (pastel) and after about 2 weeks she came around and said well it is very pretty only a few months later i got her petting it haha so if she can come around im sure anyone can. just tell your parents you aren't a kid and you want to prove it to them by being a responsible pet owner explain to them that one of the last things a BP wants to do is bite you all they do is sleep and eat haha
good luck and let us know how it goes!!