You didn't gave her a chance while she begged and willing to change for you. If you were in her place right now, would you consider getting back with yourself?
Usually, the dumpee (you are the dumper) are the one having hard time moving on with their lives, period. No matter how hard is it for you, don't ever compare what it is to her. This will only reduce the chance for you getting back with her.
3 years of memories can't be faded easily. She
might still have feelings for you. But doesn't mean she will accept you back.
I had been in a 2 year relationship. She broke it off, I tried changing and even stupidly tried giving her a second chance. But I can't be waiting forever. Now, I won't take her back.
But shes a girl, it might be different since girls usually take longer to move on rather than guys. If she still have whats called leftover feelings for you, with the right approach there are still a chance.
You know her for 3 years, you know what her likes and dislikes. Put that into good use if you want her back. Show her effort. Show her everything if you want her back. You might get lucky, who knows?