How do I add form 843 to my turbo tax? In 2021 I repaid a $5000 bonus that was received and taxed in 2020. How do I get the taxes back?

This is a claim of right repayment. You can only report it in the year you actually repaid the claim (2021 in your case).

As the repayment is more than $3,000, please read this TurboTax Help topic on how to make the claim.

I will have to file a right of repayment this year due to paying back a bonus of greater than $3000. I will have to go the refundable credit route, as I am taking the standard deduction on my taxes. I need to take the credit in turbo tax cd/ download. What version of the software do I need to purchase?

You would be able to Use TurboTax Deluxe to file the Claim of Right. 

I have already started and have almost completed my taxes in the online version.  If I switch to the downloaded deluxe edition will I be able to upload the work I have completed?

Yes. You can do this by using the Tax Tools menu option on your left menu bar in TurboTax, then Tools, then Save your return to your computer.