I read online that smoking could cause bladder damage such as cancer, but I wasn't able to find if the problem is the nicotine or the other additives found in cigarette smoke that causes the damage.
Could other sources of smoke (bonfire, paper fire, forest fire, etc) cause the same issues?
The report you have linked to also states:
The composition of cigarettes has also changed in the past few decades. While there have been reductions in tar and nicotine, the concentrations of other cancer-causing compounds have increased.
So it does look like the increase in cases may be down to carcinogens other than nicotine and tar, but don't forget that nicotine and tar are still present so they can still have an effect.
The US National Cancer Institute points out that:
Of the more than 7,000 chemicals in tobacco smoke, at least 250 are known to be harmful, including hydrogen cyanide, carbon monoxide, and ammonia.
Among the 250 known harmful chemicals in tobacco smoke, at least 69 can cause cancer.
They also cited a report of the Surgeon General (US Department of Health and Human Services, 2014). Page 228 has a big list of carcinogens in cigarettes and from page 30 the document describes how the different forms of tobacco burning during smoking creates other carcinogens and harmful materials.
Whilst it is suggested in another answer that 2-Naphthylamine is the cause, arsenic can cause bladder cancers which is also found in cigarette smoke (see page 41 of the Surgeon General's report) so you can't point to just 2-Naphthylamine.
The link above also points out many other factors which can lead to bladder cancer.
US Department of Health and Human Services. (2014). The health consequences of smoking—50 years of progress: a report of the Surgeon General. Retrieved from: http://www.surgeongeneral.gov/library/reports/50-years-of-progress/full-report.pdf
According to Wikipedia, 2-Naphthylamine is the carcinogen responsible
Thirty percent of bladder tumors probably result from occupational exposure in the workplace to carcinogens such as benzidine. 2-Naphthylamine, which is found in cigarette smoke, has also been shown to increase bladder cancer risk. Occupations at risk are bus drivers, rubber workers, painters, motor mechanics, leather (including shoe) workers, blacksmiths, machine setters, and mechanics.[14][15] Hairdressers are thought to be at risk as well because of their frequent exposure to permanent hair dyes.
which is backed up here:
There is some evidence that firefighters are at increased risk of bladder cancer, but more likely of testicular and prostate cancer and non-Hodghkin lymphoma (IARC Monographs on the Evaluation of Carcinogenic Risks to Humans, No. 98.).
