I'm not sure what you mean by store, but you can iterate over the keys using the ${!array[@]} syntax:
$ declaretypeset -A foo=([key1]=bar [key2]=baz);
$ echo "${!foo[@]}"
key2 key1
So, to iterate:
$ for key in "${!foo[@]}"; do echo "$key : ${foo[$key]}"; done
key2 : baz
key1 : bar
I found a nice, short tutorial on this here.
As pointed out in the comments below, associative arrays were added in bash version 4. See here for a Linux journal article on the subject.