First of all, since you used double quotes that print the TERM value in the current shell, not bash, you call. To do this, use /bin/bash -c 'echo $TERM' .
To set the TERM value, you can export TERM=linux before running this command, install it only for this shell using TERM=linux /bin/bash -c 'echo $TERM' (shell expression) or /usr/bin/env TERM=linux /bin/bash -c 'echo $TERM' (execve compatible (as for find -exec)).
Update: As for your editing using only the command line options on /bin/bash , you can do this without changing your input as follows:
/bin/bash -c 'TERM=something; eval "$1"' -- 'SomeUserInput'
source share