#!/bin/bash

str='-e ENV_PASSWORD="foo" -e ENV_USER="bar -e sd" -e ENV_DB_NAME="mysite_staging" '

re_pattern='-e[[:space:]]*([^[:space:].=]*)="([^"]*)"'

while [[ $str =~ $re_pattern ]]; do
    echo "variable: ${BASH_REMATCH[1]}"
    echo "value: ${BASH_REMATCH[2]}"
    str=${str#*${BASH_REMATCH[1]}=\"${BASH_REMATCH[2]}\"}
done