If I filed my Virginia state tax return before the Virginia tax bill passed, does my return need amended? It is unclear what this new tax bill changes for 2018?

No, you do not need to amend.  The Virginia DOR will send a check for this refund later this year.  Please note the following information taken directly from the tax law state document:  (link attached for the document):

In addition, this legislation provides a refund of up to $110 for an individual or $220 for married persons filing a joint return. In order to receive a refund, taxpayers need to file a complete return for Taxable Year 2018 before July 1, 2019. A refund is allowed up to the amount of a taxpayer’s tax liability after the application of any deductions, subtractions, or credits to which the individual or married persons are otherwise entitled. Such refunds are required to be on or after October 1, 2019, but before October 15, 2019.  (Bolding added)  Taken from the following document:  Tax Bulletin 19-1.