Babylon 5 was said to be neutral and was sponsored and funded by all the major powers and several in the league of non-aligned worlds. So why was the station staffed by just humans why not a multi species staff to make it more clear of it not being human bias?
I don't think it's ever made explicitly clear who funded the construction of Babylon 5, but the Babylon stations were primarily an Earth Alliance project. Following the near-catastrophic (for Earth) war with the Minbari that started over a misunderstanding, the Earth Alliance attempted to build the Babylon station as a neutral ground where humans and aliens could mingle, trade and negotiate and hopefully prevent another disastrous war. The first three Babylon stations are destroyed by terrorists before completion, Babylon 4 was completed but vanished before it could become operational. The Wikipedia entry says that Babylon 5 was co-funded by Earth and the Minbari due to the crippling financial loss of Babylon 4, but it's not clear where this is sourced from.
So Babylon 5 was essentially a human space station that was funded, maintained and protected by Earth Alliance, albeit one that existed in neutral space with a mission to provide a place that many species could co-exist and help maintain peaceful relations. Since the station crew was largely drawn from Earth Alliance military, they were all human.
That said, the station also hosts the Babylon 5 Council which consists of representatives of all the major species such as the Minbari, Centauri etc. The council was primarily concerned with inter-species relations but could sometimes rule on operational concerns of the station as well.
At one point someone, presumably Delenn, stated that the central idea of a meeting place dedicated to diplomacy is the sort of thing that only Humans would think of - everyone else, from the Drazi to the Minbari, are too self-oriented to even conceive such an idea. Between that and the fact that it is being funded and run by Earth, it's not too surprising they haven't extended rank-and-file job offers.
...until, of course, G'Kar offered the services of the Narn to round out B5's Security Forces after the station declared independence and had to purge regime elements from Security.