In the nicest possible way, you can’t simultaneously ask for a residential college, which is about as expensive as an educational placement gets, AND say he isn’t displaying any challenging behaviours.
He clearly does have very challenging behaviours, no LA is going to propose a residential placement unless they have to. It’s the difference between a placement costing 5-10k and one costing £100k.
They may feel School A can meet his needs with some additional support. They may agree an extra £10k for more 1:1. If School B is even more expensive then they won’t go for that unless the tribunal direct them.
With reference to the bullying stuff. This is obviously important. Was it ever documented? Do you have proof? And what did the bullying look like? If your son has behavioural difficulties to the extent that the LA are considering residential then I assume his behaviour must be pretty out of control. Is it possible that part of feeling bullied is about not being able to accept authority and discipline (which would then be the same problem anywhere) or are there specific documented incidents of unprofessional behaviour from staff? And if so, have you gone down the usual format complaint route (Headteacher, Gogerning body, OFSTED or equivalent?)
I’m not being mean. But if you’re going to ask the LA to shell out hundreds of thousands of pounds on this, you’ve got to have a pretty robust body of evidence as to what didn’t work at Setting A, what you did to try and make that work, and why Setting B would be any different.
I hope your son finds somewhere he can be happy 