I know it feels like the most awkward thing to mention, but your mum had to do the same when she was younger. I just waited until no one else was in the house, and just said 'mum i have started my periods' sounds obvious but there isnt really a simpler way to put it. Your mum will completely understand, dont worry.
I wandered up to my dad first, told him I was bleeding, he sighed and went to get my mother.