She is aware that I have to follow things up and she has not liked the consequences of me doing so
I'll bet she hasn't! Gives her less wiggle room to backpedal when things don't go in her favour.
I will make management aware of my revised plans, they are supportive of my methods but will not advise or intervene
As I said before, I think you do need a mentor to help guide you with this. I'm surprised your line of command doesn't allow for this.
I think it is important that she realises the consequences of her actions
Absolutely correct.
Her colleague is getting very upset and her perception is that senior management is not bothered enought to deal with this
I'm sure she is. It's so unfair and that colleague would be within her rights to raise a formal complaint herself.
I had not considered that this could be interpreted as workplace bullying
Yes, it could. I know if a colleague get making up lies about me and reporting me to the management to get me into trouble, I'd totally see it as bullying.
Its ironic as she herself has been a victim of bullying in the recent past
What were the circumstances/proof of that, do you know? It could be helpful here.
That colleague was sacked. It is now making me wonder how much was fabricated (I was not her manager at the time)
Hmmm. Does make you wonder, doesn't it? 
Could be that this person is a successful manipulator who has totally been taking advantage of the (what seems to my untrained eye) quite a lax management - I mean your managers, not you yourself -. to get away with all sorts, no questions asked and no consequences.
Having tasted success before, maybe she's ready to have another go.
I feel for you, it's a rotten situation to be in. Managing staff is never easy. I'd hate to have to do it.
Good luck!