#!/bin/bash

while getopts 'a:b:' opt; do
    case "$opt" in
        a)  printf 'Got a: "%s"n' "$OPTARG" ;;
        b)  printf 'Got b: "%s"n' "$OPTARG" ;;
        *)  echo 'error' >&2
            exit 1
    esac
done

shift $(( OPTIND - 1 ))

printf 'Other argument: "%s"n' "$@"

$ bash script.sh -a hello -- -b world
Got a: "hello"
Other argument: "-b"
Other argument: "world"