Do I need to file a tax return for Virginia if I drove Uber as a nonresident active duty military?

It may.  You are active duty military stationed in Virginia but another state is your home of record.  This TurboTax Help states:

As an active duty service member, if you worked a non-military job while stationed outside your resident state, you will need to report those wages on a nonresident tax return to that state. If you are also filing your resident return, you may get a credit on it for the taxes paid on your nonresident return.

The TaxBook, page VA-2 states:

If the taxpayer is a member of the Armed Forces, or of the U.S. Congress, who is a domiciliary (legal) resident of another state, he or she is not subject to taxation as an actual resident of Virginia even if an abode is maintained in Virginia for more than 183 days.

If the taxpayer has income from Virginia sources other than from active duty or congressional pay, Form 763, Nonresident Income Tax Return, may be required.

You are to file a Virginia Nonresident income tax return to report the Uber income if:

• the income is sourced in Virginia and 
• the gross income meets the Virginia filing requirements.

In general:

If you are considered a non-resident of state X, you generally still owe income tax on any income that you earn while physically working or living in state X.  You would report that on a non-resident return.  If you also file a tax return in the state where you are a permanent resident, you report all your world-wide income no matter where it was earned, and you can claim a credit for the taxes you paid in the other state.  

The regulations quoted for Virginia cover two different situations.

1. If you are a domiciliary resident of Virginia for 183 days, you are a Virginia resident for tax purposes even if you have a permanent residence someplace else.   The rules for domiciliary resident vary from state to state.  Sometimes, an apartment counts but a hotel does not, other times, a hotel also counts.  But, as a member of the military, you are not subject to this rule even if you kept an apartment in VA for more than 183 days.

2. Separately, if you earn income from physically working in VA, you owe VA income tax on that part of your income even if you are considered a non-resident.

So yes, you owe a VA tax return for your Uber.