Depending on where you plan to stay in Bosnia, you'll meet predominantly Christians or Muslims.
Easter and Easter Monday are public holidays there so larger cities like Sarajevo or Banja Luka will have shops and monuments closed. Most of the bars, cafes and restaurants will be open and perhaps some smaller shops.
But if you decide to you stay at smaller towns or rural areas where there's mostly Islam followers such as Travnik, Tuzla or Zenica, I believe you won't have any trouble finding an opened establishment of any type. Of course, there will still be some places that are closed not because of the Easter or the day after but because people just like to take the day off.