You state two issues here: 1) bankruptcy, and 2) owing the IRS.
I have not gone bankrupt but you will need to explain the bankrupty fully and show that you are/have resolved it. Security will want to know why it happened.
Merely owing the IRS money will not necessarily prevent you from working at a nuclear power plant, but you will need to show that you have handled it (eg., you are in an IRS installment payment plan and making payments).
If you do go to an outage take proof, like your IRS monthly statement, that you are paying and current. Even though it is on your PHQ you will need to prove it again with a piece of paper.
What is critically important is that you are completely honet on your Security PHQ and that you show you are reliable in clearing it up and dealing with it.