Chiquimula is the nearest major city (and transport hub) from the El Florido / Copan Ruinas border crossing for Honduras. You can get to Chiquimula by minibus from the border for Q20.
A bus company called Maria Elena has a daily direct bus to Flores, departing 9:30am. Goes via Rio Hondo, Rio Dulce, and Poptun. 8 hours (they'll try to tell you it takes 6), Q85. Look for their office near the main bus stand in the market.
Chiquimula is a cute little town, and quite prosperous looking. Take a stroll around the downtown area and the market.