Bash – How to convert a string into a number interpreted in certain base in bash script

I believe that this does what you want. It will put all the arguments in one string, separated by spaces, with single quotes around all:

str="'$*'"

$* produces all the scripts arguments separated by the first character of $IFS which, by default, is a space.

Inside a double quoted string, there is no need to escape single-quotes.

Example

Let us put the above in a script file:

$ cat script.sh 
#!/bin/sh
str="'$*'"
echo "$str"

Now, run the script with sample arguments:

$ sh script.sh one two three four 5
'one two three four 5'

This script is POSIX. It will work with bash but it does not require bash.

A variation: concatenating with slashes instead of spaces

We can change from spaces to another character by adjusting IFS:

$ cat script.sh 
#!/bin/sh
old="$IFS"
IFS='/'
str="'$*'"
echo "$str"
IFS=$old

For example:

$ sh script.sh one two three four       
'one/two/three/four'

Just for completeness, you don't need all those (") nor the final $(echo ...). Here's the simplified version of your assignments that produce the same effect:

STARTIME=$(date +"%T")
ENDTIME="$STARTIME today + 10 seconds"
CALL="date -d '$ENDTIME' +'%H:%M:%S'"

Note how you don't need to quote when doing var=$(...) but you do usually with var="many words":

a=$(echo 'a    b'); echo "$a" # result: a    b

Inside (") a (') has no special significance, and vice-versa, eg:

a="that's nice"; echo "$a" # result: that's nice
a='that "is nice'; echo "$a" # result: that "is nice