I took a 529 distribution in 2021 for a bill due Jan 1, 2022. Is there a way to reconcile the tax implications for this?

Just don't enter the 1099-Q.

On form 1099-Q, instructions to the recipient reads: "Nontaxable distributions from CESAs and QTPs are not required to be reported on your income tax return. You must determine the taxability of any distribution." 

When the box 1 amount on form 1099-Q is fully covered by expenses, TurboTax will enter nothing about the 1099-Q on the actual tax forms.  So, there is no way to document your situation with your tax filing.

Technically, a 529 distribution must occur in the same year the expenses were paid.  This problem, of mismatched year end distributions, is fairly common.  Treat it as received in 2022 and report it next year (you probably won't need to enter anything next year either).  And hope you can explain it away if you receive an IRS notice (unlikely).   You certainly meet  the intent of the 529 rules, if not the strict letter.  We haven't seen any reports, in this forum, of how that specific problem  has actually worked out. But, this is the usual advice. 

Do a better job on timing next year

Several users have reported receiving a CP2000 letter, from the IRS,  on unreported 529 distributions. They replied that their child was in college and the distributions were used for qualified expenses, which they listed, but they did not provide receipts. Others have reported just sending copies of the school's billing statements. They  later received a notices saying they were in the clear. I've noticed a significant drop in users, here,  reporting IRS notices about 1099-Qs, in the last two years.