You have to have one item only, no more, and this item cannot be a large machine (e.g. scuba diving equipment does not count as one item, it has many parts to it). Please also tell me how you would use the item.
P.S. Depth is 10-20m so snorkels won’t work =S
Using a baloon/bucket to trap air would be hard to hold on to because of the density of air. Therefore, suggestions like these will not work =(
As for the hosepipe idea, do you know how much energy would be required to suck air through that? And also, when you removed your mum from the hosepipe, water to go into it… =S
oops soz ppl, forgot about that, yeah, you’re underwater (20m-ish)
There is a solution to this, and anyone can do it (not just olympic swimmers or something…)

Edit – While you did mention SCUBA, your original question never said anything about being underwater. And long hoses or snokels are only good for about 1 foot underwater. The human body (i.e. diaphram) cannot draw air down more than about two feet – I’ve tried it and I am a competition swimmer.

Old answer before edit – "How about a giant balloon full of oxygen? You would just use it when inhaling. You’d exhale outside the balloon, so you wouldn’t dilute the oxygen with carbon dioxide. The balloon would only need to hold as much oxygen as your body would need for nine minutes. Probably a few liters."