although not having seen the clone wars cartoons yet, I would assume Obi-wan earned the rank of General during the clone wars, as it appears at the end of AOTC that the clones are under command of the Jedi.
I think it will be explained in the next film that Bail Organa was one of the only members of the Republican senate to remain loyal to the Jedi, once Palpatine gives the order for the Jedi to be eradicated, therefore it would make sense that Obi-Wan and the Jedi order served the republic and Bail Organa during the birth of the rebellion, shortly after they were declared public enemy number 1