I have dyed black hair and i want to go blonde?

Okay so i have been dying my hair dark for about 2 years now, (i am naturally dark blonde) its been dyed dark red to black. After having dark hair for such a long time i really want nice blonde hair for in the summer time, so i told my mum about it and i said how i would have to bleach it and everything and then leave it the bleached colour for a few days, and then dye it to the blonde i want. So i went to the shop and got a powder bleach with a 40 volume peroxide and i cut some of my hair out and did a tester (my mum wont let me do it without a tester) i left the bleach on for 90 minutes (time it said on the box) and my dark hair went to a light blonde/gingery colour, which i am happy with because after leaving my hair that colour for a few days i can dye it a nice blonde. The tester hair was also still in good condition and wasnt straw like or anything.. but now my mum said shes too worried it will burn my scalp or my hair will fall out.. do u think it will burn or fall out? i really wanted to be blonde and now i need to convince her that it will be okay.. any help anyone? :/