If I complete a coding bootcamp outside of US how would I get a job back in the states as a US citizen.

I think you can apply for jobs and get one, but don't expect to get relocation fees paid. If the office is in person and they wanted in person interviews, which is very rare nowadays, then that could be a problem as well. I would be upfront about this but saying that you would move back when you got the job. You don't want to appear sketchy that you are pretending to live in the USA while actually WORKING from Europe as that will cause HR nightmares.