If you want to ask the user for a second name, just ask the user for a second name:
#! /bin/bash
echo "Enter name of dir":
read folder1
echo "Enter name of sub-dir":
read folder2
mkdir -p -- "$folder1/$folder2"
touch docu.dat
chmod 755 docu.dat
Although I suspect that you want to create docu.dat inside the directory you just made, in which case you'd want this:
#! /bin/bash
echo "Enter name of dir":
read folder1
echo "Enter name of sub-dir":
read folder2
mkdir -p -- "$folder1/$folder2"
touch -- "$folder1/$folder2"/docu.dat
chmod 755 -- "$folder1/$folder2"/docu.dat
However, as a general rule, try to avoid prompting the user for input. That makes the script very hard to automate, very hard to re-run, it is easy for a user to enter a wrong value etc. Instead, take the directory names as arguments:
#! /bin/bash
dirName="$1/$2";
mkdir -p -- "$dirName"
touch -- "$dirName"/docu.dat
chmod 755 -- "$dirName"/docu.dat
And then run the script like this:
./script.sh "dir1" "dir2"
The -- are there so that your script can also handle directory names starting with a -. See What does "--" (double-dash) mean?.
echo "Enter another name:"; read folder2)? What else is missing? And what do you mean by "execute the script using bash parameters"? Do you mean pass the directory names as arguments to the script instead of asking the user for input?