How do I tell my mum that I am old enough to make some decisions by myself?

My mum is very nice and I love her to bits but sometimes she would get angry for no reason, If I do something by accident such as slam a cupboard loudly or knock something over (and it isn't even broken), she would still get mad!? Another thing is that me and my mum have been really close, she raised me and my brother by herself and we have been very close. However, I am 17 now and she never lets me walk out of the door to simply go down to the shop without questioning me and telling me there is no point. Also If I say to her that I want to meet friends somewhere a few miles away from my house and travel there on my bike, she would tell me "No, because you'll just get run over". This is very frustrating and undermining! I also hate it when she makes me go to places with her. Like today, she wants me to go with her and my brother and her fiance to see a horror film called Paranormal Activity. I don't want to go because I have a phobia of seeing horror films in the cinema or anywhere in general! It still annoys me that she wants me to go to places and I dont want to go! such as the park because I find them boring sometimes etc. I know she likes me around and I dont want to sound like a bratty spoilt teen because I love my mum, but how do I tell her that I am old enough to do what I want and go where I want (Within reason of course) Thanks.