How to import a variable from another script?

First of all, be aware that var and VAR are different variables.

To answer your question the . command is not bash-specific:

# a.sh
num=42
# b.sh
. ./a.sh
echo $num

The variables in "a" do not need to be exported.

http://www.gnu.org/software/bash/manual/bashref.html#Bourne-Shell-Builtins