converting finite field elements to octet strings
Ok,
if there is no standard, then "I do it my way":

Let $i$ be a root of a fixed minimum polynomial of $GF(p^2)$ and $x$ be an element in $GF(p^2)$. Then $x:= x_1+x_2*i$ can be represented as a vector $(x_1,x_2) \in GF(p)^2$. 
Now convert $x_1$ and $x_2$ with the FE2OSP function form IEEE P1363 and concatenate them
$FE2OSP(x_1)|| FE2OSP(x_2)$.  

An elliptic curve point $(x,y) \in E(GF(p^2))$ can then be represented either compressed or not compressed.

not compressed:  


$04|| FE2OSP(x_1)|| FE2OSP(x_2)|| FE2OSP(y_1)|| FE2OSP(y_2)$


compressed:


$02|| FE2OSP (x_1)|| FE2OSP (x_2)$ if $LSB(FE2OSP(y_1))=0$
$03|| FE2OSP(x_1)|| FE2OSP (x_2)$ if $LSB(FE2OSP (y_1))=1$