Bobusic made her senior debut at the 2004 Australian Open losing to American Jennifer Hopkins 6–1 6–3 in the first round of qualifying. She played on the ITF Junior Circuit for the rest of the year, with her highlight coming at Junior Wimbledon where she defeated former world number one Caroline Wozniacki 1–6 6–2 10–8.
In 2005 Bobusic played in ITF events in New Zealand, Australia, Indonesia and Thailand before she attended the University of California, Berkeley (USA), majoring in Sociology. She graduated in 2009.
Bobusic returned to Australia and competed in ITF events, losing to Sacha Jones in her first four events. She reached the final in Darwin and lost in the semi-finals in Port Pirie. She ended the year ranked 441.
Started the year playing in ITF events in Australia and Korea. Bobusic played ITF events in America in June and July, but only won one of the six matches she competed in. Bobusic returned to Australia and entered seven ITF events, only winning two main draw matches, both in Alice Springs. She finished 2010 with a win-loss record of 10–17, and dropped to 596 in the WTA rankings.
Started the year by qualifying for five consecutive 25k ITF events in Australia, winning a main draw match in Mildura and reaching the quarter-finals in Bundaberg. Bobusic travelled to America again, and reached her second and third ITF finals at 10k Landisville and 10k Hilton Head Island. She then played in three events in Great Britain and lost in her fourth career ITF final at 10k Chiswick to Croatian Donna Vekić, 3–6 6–3 6–3. She returned to Australia and had a successful end to the year, reaching two 25k semi-finals, losing her fifth ITF final to Australian Olivia Rogowska 6–3 6–2, and winning her first ITF title in her sixth final at 25k Mount Gambier against Korean Han Sung-hee 6–3 6–2. She received direct entry into Tennis Australia's annual Australian Open Wildcard Play-off, where she defeated Viktorija Rajicic and Sally Peers and was beaten by Storm Sanders in the round robin stage. In her semi-final, Bobusic lost to defending champion Rogowska 6–4 7–5. Bobusic finished 2011 ranked 294, the highest year-end ranking of her career.
Bobusic benefited from her career-best season in 2011 by receiving qualifying wildcards into the Brisbane International and Moorilla Hobart International. In her WTA debut, Bobusic faced Russian Nina Bratchikova and lost 6–1 7–6. Against Heather Watson in Hobart, her first ever top 100 opponent, Bobusic lost a close match 3–6 6–3 7–5. Her first main draw appearance in a Grand Slam at the Australian Open ended with a 6–1 6–3 loss to German 30th seed Angelique Kerber.
Following the Australian season, Bobusic didn't play for four months due to plantar fasciitis. She returned to the ITF circuit in June 2012, achieving mixed results for the remainder of the year. Her final tournament In 2012 was the Australian Open Wildcard Playoff tournament, which she won, defeating three higher-ranked opponents including 2nd seed Ashleigh Barty, 4th seed Arina Rodionova and 3rd seed Monique Adamczak. The tournament win secured Bobusic a wildcard in the 2013 Australian Open.
Bobusic's win in the Australian Open Wildcard playoff helped her to gain a wildcard into the qualifying draw at the Brisbane International. It was only the third time she had played in a WTA tournament. She drew fellow wildcard recipient Arina Rodionova in the first round of qualifying and won in three sets. In the second round she defeated Karin Knapp of Italy in a match lasting over three hours. She then defeated 6th seeded Kristýna Plíšková in three sets to qualify for the main draw of a WTA tournament for the first time. She drew world #44 Alizé Cornet in the first round and lost in three sets.
Bobusic's strong performance in Brisbane help her to gain a wildcard to the main draw of the Hobart International where she lost a tight match to qualifier Lauren Davis (USA) in the first round in three sets. In the doubles event in Hobart, she reached her first WTA doubles semi-final, partnering Ashleigh Barty.
Bobusic received a difficult draw at the Australian Open, drawing 4th seed Agnieszka Radwańska. Bobusic played well above her ranking and served for the first set, before losing in straight sets.
Bojana announced that because of chronic back and foot injuries, she will not play professional tennis anymore. Her last match was at Hopman Cup (3 January 2014) where she played together with Oliver Anderson, they were replacing players form United States team – Sloane Stephens and John Isner.