I am Indian and next month I am traveling from Split to Dubrovnik via bus. I have a Schengen visa. The bus in between goes to Bosnia and Herzegovina which is not part of EU / Schengen. Will I be able to board that bus?`
Yes, if your Schengen visa is valid for multiple entries. People with multiple-entry visa for a Schengen country (or an EU country or the US) may enter Bosnia and Herzegovina on the basis of that visa for a stay of up to 30 days (yours will be more like 30 minutes).
(1) Citizens of the countries with whom Bosnia and Herzegovina has a visa regime, may enter Bosnia and Herzegovina with passport, without the obligation to obtain a visa for entry, exit, transit and stay on the territory of Bosnia and Herzegovina upto 30 days only if they have a valid multiple entry visa or residence permit issued by the signatory countries of the Schengen Agreement, the EU member states or the United States of America.