Notation for the ith row and column of a matrix When noting the $i^{th}$ scalar of a vector $\mathbf{x}$ one usually does it as $x_i$, since it is a scalar
When doing this for matrices that are being denoted in bold, let's say $\mathbf{A}$, how should I write the $i^{th}$ row or $j^{th}$ column?
This question provides some insight as to how to distinguish  from rows and columns but does not address any possible standards for doing it as $\mathbf{A}_{i*}$, $A_{i*}$ or maybe even $\mathbf{a}_{i*}$
Is there a preferable form?

There is no standard notation. Depending on the assumed lectureship you could use
${\rm row}_i( A)$ or $ A_{\,i\,\cdot}$ for the row matrix  $[a_{i1}\>a_{i2}\>\ldots \>a_{in}]$,
and ${\rm col}_j( A)$ or $ A_{\,\cdot j}$ for the column matrix $$\left[\matrix{a_{1j}\cr a_{2j}\cr\vdots\cr a_{nj}\cr}\right]\ .$$
You then would have, e.g.,
$${\rm elm}_{ij}(AB)={\rm row}_i(A)\cdot{\rm col}_j(B)\ .$$
