You can currently use the Hungary and County passes on local buses in these cities:

Local transport: County passes can also be used on local transport (metros/trams/buses) in the following cities: Budapest, Csongrád, Debrecen, Ercsi, Esztergom, Érd, Miskolc.

Daily tickets do not allow you to use local transport except Érd and Csongrád (although you can use interurban services between stations within any city).