So I have some time now to put together an example and I think I might know what ADP wants you to do. Keep in mind that all of this is just a fix for doing the bonus wrong this year. If you want to pay a bonus next year, just put the gross amount in the payroll system and let it get taxed, and it will cost the company 7.65% employment tax like all the other wages, or reduce it by a few percent and put it in the payroll system and let it get taxed like usual.
Let's look at Mary whose salary is $1000 per week. Her normal check looks like this:
(Example 1) Gross $1000
FICA and OADSI $75
Federal withholding $200
State withholding $50
Net pay $675. (Note the employer pays a $75 employment tax match on form 941.)
If you had taxed the bonus correctly, her check would look like this:
(Example 2) Gross $1200
FICA and OADSI $90
Federal w/h $250
State w/h $70
Net pay $790 (Note the employer pays a $90 employment tax match on form 941, so the bonus actually costs the employer $214.)
Now because you handed her the $200 on the side, you need to pay employment tax and you were supposed to collect withholding. It sounds like ADP wants the employer to pay it all so it doesn't have to come from the employee, like this:
(Example 3) Gross pay $1000
Gross up for taxes on bonus $85
FICA and OASDI $75
Federal w/h $200
State w/h $50
Additional federal, state and FICA withholding for the side bonus $85
Net pay to employee $675.
The employee gets to keep the bonus in full and the employer pays the tax that should have been withheld but wasn't. But now the bonus costs the employer $300 instead of $215.
But there's another way to do it,
(Example 4) Gross $1000
FICA and OADSI $75
Federal withholding $200
State withholding $50
Additional FICA due on bonus $15
Additional federal w/h due on bonus $50
Additional state withholding due on bonus $20
Net pay to employee $590.
Here, the employee takes a last minute haircut in their check due to the employer's mistake. Their last check of the year is cut by $85. But, this represents the correct withholding on the untaxed bonus, so they still come out $115 ahead, even though they are likely to be pissed off. And the state and federal withholding represents tax they owed anyway that would have come out of their refund if it was never withheld. ADP should agree to do this rather than insisting that you pay all the taxes as in example 3. Your employees may howl, however, and this will need to be explained carefully and sympathetically. It may be worth it to gross up the bonuses as in example 3 just to keep up morale. That's just something to think about. Remember, this only happens this year. Next year you will pay the bonuses properly following example #2.
There is a final possibility:
(Example 5) Gross $1000
FICA and OADSI $75
Federal withholding $200
State withholding $50
Additional FICA due on bonus $15
Net pay to employee $660.
Here the employee is only taking the haircut on the FICA and OASDI. This is tax you MUST collect. It leaves the income tax withholding uncollected. This puts you in violation of the law regarding how lump sum bonuses are supposed to be withheld. And it means that the tax due will come out of the employees' tax refunds instead of being withheld in advance. But it has less of an immediate impact on their paychecks. ADP may require that you follow the law (example 3 or 4) or refuse to process your payroll, I don't know. But they may be willing to go along with #5 on the grounds that the harm is already done, and #5 minimizes disruption to the company and the employees. They may want you to sign a waiver of responsibility advising you this is incorrect and that you relieve them of responsibility.
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Anyway those are some things to think of. If you are forced by ADP to go with #3 or #4, you might be better with #3 for morale, and then skip bonuses for one year if you have to. Remember this is a one-time problem and future bonuses will not cause this problem if handled correctly (#2).
Good luck.
