Let some other folks reply before you take this and run with it, but my thoughts:

I'm assuming you expect the coefficient of BS to be negative if you are using:

Sales of WS = β1 (Price of WS) - β2(price of BS) + constant as the model.

That is, you need to make sure that as price of BS is rising that sales of WS is also increasing. Since the two are substitutes, a rise in the price of one, all else held constant, should create a drop in demand for that product and substitution towards the other.

The log is being use because the demand curve is likely curvilinear. This transforms the data to something more linear to properly meet regression linear requirements.

I haven't given it great thought, but I'd call B1 the price elasticity of demand for WS and B2 the cross price elasticity of demand.

Keep in mind, however, that elasticity changes at different points along the demand curve. Unless the demand curves are iso-elastic (unlikely), the model may not be all that good for inference too far beyond the mean, though this is just conjecture on my part. Let someone else verify this assumption... and all my others for that matter. Taking the log may ameliorate this issue, though I'm not sure and its too far past my bedtime to think about it.

I'll let you do your own homework..... Look at dummy variables and consider if they may be useful.