Outside of Linux land or lacking access to the /proc filesystem or equivelent, you can make use of pstree:
Assuming you have the pid of
On a Mac:
./test.sh
16012
-+= 00001 root /sbin/launchd
\-+= 00245 wingwong /sbin/launchd
\-+= 04670 wingwong /Applications/Utilities/Terminal.app/Contents/MacOS/Terminal -psn_0_2052597
\-+= 11816 root login -pf wingwong
\-+= 11817 wingwong -bash
\-+= 16012 wingwong ksh ./test.sh
\-+- 16013 wingwong pstree -p 16012
On a Linux box:
./test.sh
14981
bash(14981)---pstree(14982)
The format and style of the output from pstree differs, depending on your environment, but you can enforce ASCII output and then sed/tr/awk/etc. filter the output to get the shell that is running the script.