Taming older parakeets?

When I first got my parakeet around 6 years ago we had a tragic incident where she left her cage and I had to chase her outside. After that she's been very scared of me and ever since has had an aggressive behavior towards me. Whenever I try to rest my hand in her cage (not attempting to go near her) she comes to my hand and bites aggressively.

Because of my busy schedule, I haven't been able to spend much time with her everyday and things always seem disappointing when I try to interact with her.

It's been around 6 years now and I really want to tame my bird. Is there any way to tame a parakeet after having her this long? Or is it too late? :\

I'm going to the store today to buy her new toys and cage accessories. If there's any tips out there, I'd really appreciate it!