You are confusing a few things.
There are two filing options for married couples: “Married Filing Jointly” and “Married Filing Separately.” (There is a third filing option called “Head of Household” that one of you might use if there are children involved.)
Married Filing Jointly (MFJ) means that you file one (and only one) tax return for the both of you.
Married Filing Separately (MFS) means that, although you are married, you are each sending in your own return.
So, first, you need to be clear about your filing status. Either you both work together to file one return (MFJ), or you each file your own return (MFS). If you aren’t giving your tax documents to your wife and she isn’t giving you hers, then you both need to file Married Filing Separately.
When you file MFS, there are a few things you still need to coordinate between the two of you. If there are children/dependents involved, you will need to come to an agreement about who is claiming them on their tax return, as only one of you can claim each dependent.
And, related to your question, if one of you decides to itemize deductions as MFS, the other cannot take the standard deduction; he or she would be required to also itemize, even if it results in a lower deduction amount than the standard.
As mentioned above, there is a third filing option called Head of Household that can possibly be utilized by one of you if there is a child involved and all the requirements are met. One of the features of Head of Household is that it allows a standard deduction even if you are technically married to a spouse that has itemized.
For more information about taxes while you are separated, see IRS Publication 504, Divorced or Separated Individuals.
Finally, as Glen Pierce and Hart CO have mentioned in the comments, the term “itemized deductions” refers specifically to the deductions that are listed on Schedule A. It has nothing to do with your business’s Schedule C. So you still need to determine whether or not you will be taking the standard deduction or if you will be itemizing on Schedule A.