I am also a novice in this field, but I think that it depends on the algorithm. If the neural network makes use of a stochastic gradient decent for example, then random initial weights (between 0 and 1) will work just fine, as the weights will converge automatically each learning step. This number of learning steps required is often in the same range, but may depend on some parameters in your model like learning rate and connection strength etc., while random starting weights will make sure that there is an output of each layer in the network for every input pattern.
I am not sure about the term, bias. From what I know, bias is often used in a more Bayesian type of framework. I would advice you to read up on any material from Machine Learning/ Computational Neuroscience courses. This can be a text book or any other online material.
