Try doing this, there's no special character to concatenate in bash :
mystring="${arg1}12${arg2}endoffile"
If you don't put brackets, you will ask bash to concatenate $arg112 + $argendoffile (I guess that's not what you asked) like in the following example :
mystring="$arg112$arg2endoffile"
The brackets are delimiters for the variables when needed. When not needed, you can use it or not.
bash > 3.1)
$ arg1=foo
$ arg2=bar
$ mystring="$arg1"
$ mystring+="12"
$ mystring+="$arg2"
$ mystring+="endoffile"
$ echo "$mystring"
foo12barendoffile