The apostrophe here makes sense as Neal points out.
However, it is so because word bro is the elided form of brother, like typo, porno or even zoo. Hence the apostrophe makes more sense here with regard to the word being elided than with the -o ending, again compare with folios, videos, trios and cellos. Inflexions in -s before a -o can lead to adding an -e- as with cargoes and volcanoes.
I don't know if there is a strict rule for the -e- infix, but in the case of elided words it seems unnecessary.
In the end dictionaries show bro can become bros in the plural. It might just be a matter of style or an orthography in transition. The beautiful thing about living languages, is that you take part in their making. So the choice is yours I would say.