Hmm, I'm with the people who speak of karma - what goes around, comes around (though sometimes in unforseen ways)... What you give out to the Universe, may come back to you... (which the lady at work may have been experiencing already..) Maybe her being a bully has to do with home situation too.. People who are generally happy with life and themselves usually don't go around bullying other people..
It's okay to be furious and angry if someone behaves in inappropriate ways to you, it's okay to protect yourself and be assertive and do constructive problem solving if possible... If the person has problems, it's kinda 'natural' and only human, to think something like 'well, serves her right'... to call people 'crazy bitch' or such, seems offensive though.. and it is good to raise yourself above her level..
James, it's okay to acknowledge anxiety disorder, it's not a very good idea to 'hide' behind it, though.. Dividing people into 'them' and 'us' can quickly lead to even more misunderstandings and things like one group feeling superior over the other.. Yes, bullies have a problem too, sometimes even bigger problem than the 'victims' - they may get fired for their behaviour too, and their personal relationships may suffer.. Maybe it's good to remember that it's just different 'defense mechanisms' - it's not the real 'you' or 'them' - in the same threatening situation, some people may go shy/depressed, while some may go 'aggressive'.. Also, people are not just 'good' or 'bad/evil', there are tons of different shades of grey and all colors inbetween..
Both may need to learn better ways of communication, I recommend the book Dealing with Difficult People.. It's easy to fall into the 'accusation' trap, if one needs to work with this person, it's better to find some tips how to work with them in more constructive ways... There are work bullying support websites too, communication workshops, maybe even personal coaches or such..
Some schools have anti-bullying programs & policies, I hope some businesses too??