The BB singularity (and Black Hole singularities for that matter) always strike me as being essentially unphysical. For a start there is the Plank length (~10^-35) below which supposedly it is impossible to describe the physical universe. If I recall correctly it arises from the Uncertainty Principle.
My personal veiw is that singularities arise because we treat space-time as continuous i.e. infinitely divisible. This is fine for mathematical purposes but physical "reality" may be that space-time is quantized (possibly with quata of the order of the plank length).
My understanding is that String/Brane Theory avoids singularities because of a similar type of quantization.
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