Should I receive a 1099? I am a contract bookkeeper. I was paid over $600 and the company paid me directly with a bank transfer.

Yes, if you are an independent contractor, not a corporation, and were paid more than $600, the company that paid you should issue you a 1099-MISC that you report on your tax return.  In QuickBooks, your vendor profile should indicate that you are 1099 eligible.  

I am set up correctly in QBO. For whatever reason, it's not recognizing that I should have been issued a 1099.

Yes, the company should send you a 1099.  Its easy to forget to include yourself when you're doing the books! 

All you need to do is print out a blank form 1099 (from IRS.gov), fill it out, check the "Corrected" box, and mail to the IRS.....and keep your copy of course!

Thank you!