Rita-

You should always be able to charge the county rate.  Copy costs are driven by the client requirements, whether it is a full pages or pert pages for certain documents.  You should never have to charge less than what you paid to acquire them.  I personally would bill for your search fee and the copy cost fees and if they don't pay, then I guess you have your answer as to whether or not you'll provide work for them again.  Maybe the take away going forward is that we all need to verify in advance for new clients if they are going to pay copy costs at the county rate.   I suppose you could always raise your rates to balance out underpayment for copy costs and charge a dollar per page if they are really insistent that's the most they'll pay.  :)  Good Luck!