What is the process for prior service to put in an exception to policy to skip BCT?

Exceptions are for exceptional people or circumstances.
What's so exceptional about you or your situation that warrants an exception?

No offense to anyone on here but they are misinformed. I'm looking at going back in myself. A simple google search of current Army directives will answer this question.

I think you should review and bring Army Directive 2019-31 (current as of Oct. 2019) to your recruiters or commands attention.

I've included the link. Either a waiver or According to paragraph 5 and 7 you only need to attend a PSRC “Prior Service Refresher Course” as established by the Commander, Training and Doctrine Command. Also see enclosure 2 paragraph 3 and enclosure 4 (the last page) makes it very clear and cut what applies to who and what.

https://armypubs.army.mil/epubs/DR_pubs/DR_a/pdf/web/ARN19498_AD2019-31_Web_Final.pdf

IMO there's absolutely no reason an Army combat vet should have to repeat basic training with a bunch of 17 and 18 years olds and I think the Army agrees which is why they have the "PSRC"

With you coming back in with a 4 year break in service (2008+8, IRR time counts) you will definitely have to go back through. Coming from someone who has done basic training twice, it's not that big of a deal if your motivation is pointed in the right direction. Best place to get all that info is in the reg, especially because it changes so often.