I believe both states or part of the Motor Vehicle Compact
and reporting may/will occur post conviction.
What Virginia will do with it is probably up to the standards of that Commonwealth's D.O.T.
I first suggest you make a call to VA DOMV
and inquirer whether or not out of state convictions affect your VA MVA and if points are assessed (I believe this varies from state to state).
Based on that answer (preferably in print) then you would be in a better position to discuss the particulars with representatives of Ohio.
If you are living/staying (even temporarily) in Ohio, then perhaps a court appearance would be merited. If have found that negotiations for reduced convictions can often be accomplished without the need for a lawyer, provided you were decent at the time of the traffic stop. Often times with reduced pleas come reduced fines (meaning you may even get a bit a refund).