There are a couple buses a day operated by Jadran Ekspress Kotor from Mostar to Podgorica for sale on the Montenegrin bus ticketing site BusTicket4.me
Don’t think there are direct bus services from Mostar to Podgorica. There are buses from Mostar to Budva once daily (5.23 hrs) and then from Budva to Podgorica every 20 minutes (1.32 hrs). See this website for more details:
http://www.rome2rio.com/s/Mostar/Podgorica
This link might be also useful: http://wikitravel.org/en/Mostar
Credit:stackoverflow.com‘