Preface: copy as you go, improve as you go.

#!/bin/bash

unset ANSWER NAME DIR
echo -n "Record or not? [y/n]:"
read ANSWER
while [[ $ANSWER != 'y' && $ANSWER != 'n' ]]
        do
                echo "What you have entered is neither 'y' or 'n', Please enter again:"
                read ANSWER
        done
if [ $ANSWER = 'y' ]; then
        echo -n "Please enter the name:"
        read NAME
        [ -z $NAME ] && NAME=`date +%Y%m%d%H%M` && echo "Got Nothing! Use the default ($NAME)."
        echo -n "Please enter the directory to store these files:"
        read DIR
        [ -z $DIR ] && DIR="/var/log/script" && echo "Got Nothing! Use the default ($DIR)."
        [ -z ${DIR##*/} ] && DIR="${DIR%/*}"
        [ -d $DIR ] || mkdir $DIR
        exec /usr/bin/script -t 2>$DIR/$NAME.time -a -f $DIR/$NAME.log
        echo "$?"
        [ $? -eq 0 ] || echo "error!!!" && exit 127
else
        echo "Thank you!"
fi
unset ANSWER NAME DIR

Exit shell record:

$exit

Replay the recording (replace with the actual time and log file):

$ scriptreplay TIME.time LOG.log

View the record:

$more LOG.log