Do you have a garage or car port where you could hang it? If you can save up enough you can get a bag with a stand that the bag hangs from. Or even one of those free standing bags which you could use in your damn bedroom. If you want I can send you a few links to some bags for sale online which won't require hanging up anywhere, or much space (depending on how much you want to dance around it). Speed bags can be mounted onto solid walls. Don't know if your mum would like you drilling holes into your walls though at home.. There are always ways around things though if your determined.
You can always work on the excuse to your mum that it's a hell of a lot safer letting you learn to fight and DEFEND YOURSELF in the CONTROLLED safety of a gym, compared to bully's in the real world where you could suffer a LOT more damage. It worked with my parents when I was younger.