My dog has recently started to bark at one neighbour, she is not being very nice about it and makes him worse by shouting at me every time he barks at her any ideas on how i can stop him as i have to keep him whenever she is out in her garden.

To start with, tell her you are working on the problem.  You realise it's a problem and are doing something about it and taking advice.......

Is the dog barking because he can see her or hear her?  Can you reward him (perhaps having him on a lead to start with, so you have some control over him) for NOT barking?  Distraction often works to break the cycle - clap to get his attention, call him to you, do a few brief training type moves - 'sit/down' etc, then reward him and send him on his way....

HTH

If he's outside without supervision, are you absolutely certain that he hasn't been provoked - ever? some dogs have long memories ;)

How high is your fence? would it be worth putting a bigger fence up then the neighbour cant see over and if the dog is still barking at her its because shes looking over.