Do I have to go through Bosnia and Herzegovina to get to Dubrovnik, Croatia? Can I use a double Schengen visa? Thank you ?

Yes, it's about ten kilometers. You must hold a Schengen visa with multiple entries. Do you have two? Generally, they are either single S or multiple M. If you enter any Schengen country twice, it will be counted as one entry. If you go back and forth via Bosnia and Herzegovina, it will be counted as two entries, which may not be allowed.