The inter-entity border between the Federation and Republika Srpska is not controlled and is essentially not very different from U.S. state borders considering its impact on travel.
The best way to get around with public transport is with bus and train Federation (http://zfbh.ba, RS (http://www.zrs-rs.com/)). There is a dense network of bus lines, all run by relatively small private companies. Be aware that if you buy a return ticket for a line which is served by more companies, you can only make the return trip with the company you bought the ticket at.
Trains are infrequent and slow. Many train lines were damaged in the war, and have not yet been rebuilt. There is also a lack of carriages and trains to provide frequent services - even on the busy lines like Mostar-Sarajevo, Tuzla-Banja Luka and Sarajevo-Banja Luka. However, the rides are scenic, especially that Mostar-Sarajevo stretch.
Hitchhiking is fun in Bosnia as you will get rides from local people who you won't much encounter through hospitality exchange networks as couchsurfing. Be carefull though for landmines, and if you're not sure, stay on the paved road, and ask locals "MI-ne?".
Cycling is beautiful in Bosnia. Other traffic is not so much used to how to relate to bikes on their way, though.
Google Maps, an online mapping resource, is very rudimentary present in Bosnia. However, volunteers are mapping Bosnia in Open Street Map, and at least the maps of the main towns in Bonia have a lot more detail than those of the maps of the US-based company.
If you are looking for detailed army maps, you can find a list on the site of the army: (http://www.armijabih.com/...)