This study was published in February 2015 in the journal Urology and evaluated the records of over 80,000 participants in a multi-ethnic California Men's Health Study cohort of men aged 45-69.
Information on demographic and lifestyle factors including smoking history and cannabis use was collected using mailed questionnaires between 2002 and 2003. They linked the study data with clinical records including cancer data from electronic health records.
In summary, tobacco use increased the chance of bladder cancer, but cannabis use only (no tobacco) was associated with a 45% reduction in bladder cancer occurrence. In short, cannabis use may help reduce bladder cancer risk, and tobacco definitely increases the risk.
"After adjusting for age, race or ethnicity, and body mass index, using tobacco only was associated with an increased risk of bladder cancer, whereas cannabis use only was associated with a 45% reduction in bladder cancer incidence. Using both cannabis and tobacco was associated with an HR of 1.28 [28% increase]".
The abstract is here at the NIH National Library of Medicine site.