@Arjen,
Someone asks, "What is Plato's position on education"" This question is different from "What is Plato's philosophy?" because it is asking a question about Plato's thinking about a specific topic. We are not inquiring about Plato's philosophy taken as a whole, but about a part of it that is relevant to what we are considering.
In general, then, a position is a thinking about a particular branch of philosophy, or a specific issue, or another philosopher's writing. Sometimes the untutored ask a speculative question, such as "what would be (note the future conditional) Plato's position on abortion?" that asks one to apply doctrines of his philosophy to conditions he had not considered.
Now how these positions are developed depends not only upon how one views philosophising itself, but as well on one's own epistemological "position." I would suggest that a philosophical position begins as a process of investigation and thought until it takes shape, is tested against other positions (both of earlier philosophers and just as importantly against other positions one holds since a position must be consistent within a system of thinking), and lastly undergo revision in the light of new perspectives or new information. This is somewhat, and not to press the point, akin to Hegel's triadic movement of thought: thesis, antithesis, and synthesis the latter "including" the antithesis.
I think, lastly, that one should avoid the use of the term "bias" because of its unsavory connotations. While it may be that some philosophical positions may in some fashion influence or colour the way things and events are understood, it does not necessarily follow that either this happens in every instance, or that it
must do so; a philosophic mind should be able, in its quest for truth and precision, to "bracket" this influence.