Also, you have to stop mistaking the Republic for a unified entitiy- it is a coming together of Sovereign worlds, more like the UN than a single country. This is why it doesn't have a single army for most of its history, the closest being the Jedi (who, incidentally, were at one point in the design stage for TPM decked out in UN peacekeeper style uniform).
So this is not like a US Senator ordering a US General. When Palpatine uses emrgency measures to create a Republican army- based, obviously, on the Clones- in AOTC, they would be looking for all sorts of talented people for high command. Bail may represent Alderan at the Senate but that in no way de-bars him from taking military rank under these circumstances.
Alternatively, Obi-Wan may not be taking ORDERS, as such, but powerful politicians like Bail may be, under Palpatine, directing the war effort, in which case Obi-Wan might be one of the Generals responsible for carrying out Bail's objectives- wars are run by politicians, after all.