$x$ co-ordinates of two points $B$ and $C$ are the roots of equation $x^{2}+4x+3=0$ and their $y$ co-ordinate are the roots of equation $x^{2}-x-6=0$. If $x$ co-ordinates of $B$ is less than $x$ co-ordinate of $C$ and $y$ co-ordinate of $B$ is greater than the $y$ co-ordinate of $C$ and co-ordinate of a third point $A$ be $(3,-5)$, find the length of the bisector of the interior angle at $A$ ?