interest rates - Bond-price dynamics in the Vasicek model

Hello I am studying about interest rate modeling

There is one good source about Vasicek (link: https://web.mst.edu/~bohner/fim-10/fim-chap4.pdf). However there is one equation that I try but unable to replicate which is:

$dP(t,T) = r(t)P(t,t)dt - \sigma B(t,T)P(t,T)dW(t)$

This equation on 2nd page (or page 18th according to document paging). It locates about 1/3 page top down. Anyone understand how we get this one? What border me is why there is $B(t,T)$ appear. I tried but unable to obtain that result.

Besides, the side question is why in interest rate stochastics process it is always express under risk neutral $\mathbb{Q}$ why a traditional stock price S is often expressed in $\mathbb{P}$

Thank you so much