Rail passes do not cover all towns but there are country/city busses. Is there a monthly pass for ALL of DK for bus use? Thanks!
Yes there are monthly passes, but they are for commuters and would be valid for a particular route or particular zones. All public transport is under the same ticket system, so tickets are valid for trains, metro and busses. There some private bus companies like flixbus, that run long distance busses, don't know if they have passes. Where are you planning on going?
(almost) all buses and trains in Denmark accept the "rejsekort". I suggest you get one when you enter Denmark.