It is almost always the case that ABA would work within or alongside mainstream school. One of the purposes of ABA is that it aims to teach children the skills needed in mainstream life, so to remove children from that kind of works against that principle. Exceptions are of course ABA schools. But on the whole, most programmes work towards the aim of genuine inclusion and participation in ms schools.
We do a light-version of ABA in ms school, ds goes full-time. Like fauxfox, we have trained a TA provided by the school. Others might bring in their own tutors (who can be e,mployed by the school).
The number of hours depends on what you can afford (if self-funding), and how intensive a programme your child needs.
The path to getting ABA in mainstream school is anything but straightforward, sadly. Most families start doing a programme (often at pre-school age), have to demonstrate that it works, then fight the local authority for funding. It is almost unheard of for a LA to offer to fund it without a fight - most have to go to tribunal to get it. Even that is not a guarantee.
This is because the cost of an ABA programme (inc tutors, supervision and consultant) is much more than the minimum salary for bog-standard TAs.
There is also the consideration of how supportive the school will be of having 'outside' experts coming in working with your child. Your school sounds supportive, which is a good start.
If I was you first step would be to look into ABA providers (either organisations like Peach or UKYAP) or independent consultants to discuss a programme - first things to decide are how it would be tailored to what your ds needs, how much you can afford, how it will be work within the school. Next step is getting school/LA to fund it!