How can I save my response into a list in BASH?

First of all you can simplify the jq query to process the EC2 output in one go.

#!/usr/bin/env bash

# Map the output of jq parsed EC2 response into the $regionList array
mapfile -d '' regionList < <(
  # Gets EC2 response in JSON piped
  aws ec2 describe-regions |

  # Processes JSON into a null-delimited stream
  jq --join-output '.Regions[] | .RegionName + "\u0000"'
)

# Iterates the list
for regionName in "${regionList[@]}"; do

  # Do stuffs with $regionName
  printf 'Doing stuff with: %s\n' "$regionName"
done

You could create a single jq command to save the output into an array. Afterwards you can iterate over it with a for loop:

#!/bin/bash

awsRegionList=($(aws ec2 describe-regions | jq -r -c '.Regions[] | .RegionName'))

for region in ${awsRegionList[@]}; do
    echo $region
done;

Note, using -r will remove the quotes as well, so the output will be something like:

eu-north-1
ap-south-1
eu-west-3
eu-west-2
eu-west-1
ap-northeast-3
ap-northeast-2
ap-northeast-1
sa-east-1
ca-central-1
ap-southeast-1
ap-southeast-2
eu-central-1
us-east-1
us-east-2
us-west-1
us-west-2