Per the IRS instructions on filing as Head of Household as a Citizen Living Abroad, if you choose to file only your own taxes, and you qualify for Head of Household without them, the IRS does not consider you married:
If you are a U.S. citizen married to a nonresident alien you may qualify to use the head of household tax rates. You are considered unmarried for head of household purposes if your spouse was a nonresident alien at any time during the year and you do not choose to treat your nonresident spouse as a resident alien. However, your spouse is not a qualifying person for head of household purposes. You must have another qualifying person and meet the other tests to be eligible to file as a head of household.
As such, you could file as Married Filing Separately (if you have no children) or Head of Household (if you have one or more children, a parent, etc. for whom you paid more than half of their upkeep - see the document for more information).
You also may choose to file as Married Filing Jointly, if it benefits you to do so (it may, if she earns much less than you). See the IRS document Nonresident Spouse Treated As Resident for more information. If you choose to treat her as a resident, then you must declare her worldwide income. In some circumstances this will be beneficial for you, if you earn substantially more than her and it lowers your tax rate overall to do so. Married Filing Separately severely limits your ability to take some deductions and credits, so it's well worth seeing which is better.