Bias is how it's called the presence of a leaning on a speech, affirmation, etc. This word usually bears a negative tone.
Reliable means that an affirmation, speech etc. is trustworthy, that is, it doesn't have a bias -- it isn't one-sided.
It is important to keep in mind that humans are rarely able to be completely reliable. We are always biased despite being conscious of it or not. Thus it's important to take this into consideration when you are studying history and is reading an old source, for example, or when you are reading a newspaper. Reliable information is achieved by weighing biased affirmations and seeing beyond them.
