Bash regex capture group

It's a shame that you can't do global matching in bash. You can do this:

global_rematch() { 
    local s=$1 regex=$2 
    while [[ $s =~ $regex ]]; do 
        echo "${BASH_REMATCH[1]}"
        s=${s#*"${BASH_REMATCH[1]}"}
    done
}
global_rematch "$mystring1" "$regex" 

1BBBBBB
2AAAAAAA

This works by chopping the matched prefix off the string so the next part can be matched. It destroys the string, but in the function it's a local variable, so who cares.

I would actually use that function to populate an array:

$ mapfile -t matches < <( global_rematch "$mystring1" "$regex" )
$ printf "%s\n" "${matches[@]}"
1BBBBBB
2AAAAAAA

To get the second array value, you need to have a second set of parentheses in the regex:

mystring1='<link rel="self" href="/api/clouds/1/instances/1BBBBBB"/> dsf <link rel="self" href="/api/clouds/1/instances/2AAAAAAA"/>'

regex='/instances/([A-Z0-9]+).*/instances/([A-Z0-9]+)'

[[ $mystring1 =~ $regex ]]

$ echo ${BASH_REMATCH[1]}
1BBBBBB
$ echo ${BASH_REMATCH[2]}
2AAAAAAA