However, Jira fundamentally is about managers tracking work, and not about workers actually getting stuff done. There's no way I can track all my tasks in Jira even if I have a nicer GUI for it.
I'm actually part of the way towards writing a program to sync tasks between Asana and Jira using their APIs. I'm hoping that that'll let me continue working in Asana while it handles Jira (which I've always found incomprehensible) for me.
You can create your own lists inside of Bee which filter issues based on your own rules (http://neat.io/bee/docs/smart-lists.html). It's helpful because you just define the rules one-time and then flick to it whenever you need to.
Bee also has a menubar helper which tracks your short-term tasks and queues up your next issue so you always know what you're working on (http://neat.io/bee/docs/the-short-list.html).
Also you can add your own Notes list which is just a series of text files (easily synced via Dropbox) if you want to track your own local tasks.
I'm constantly iterating based on user feedback so if you have time, please let me know how it works out for you :)