Your extenuating circumstances sound strong to me, and 'recent rapid progress' is a good argument at appeal.
However, bullying should not take up more than 50% of your appeal - you will need to present a very strong academic case too. This could be based on evidence that pre-dates the bullying, and on hard evidence of recent rapid progress in key subjects such as maths and English.
The wider the range of evidence, the better. See:http://www.elevenplusexams.co.uk/appeal ... cation#b11
Bearing in mind that any school you appeal for may be oversubscribed, you will also need to prepare good reasons for wanting a place at the school in question. See C2a:http://www.elevenplusexams.co.uk/appeal ... -school#c2
You would be well-advised to study the Q&As as a whole:http://www.elevenplusexams.co.uk/appeals