Addition: an EC2 instance is needed also for the bot. A t2.medium instance in us-east-1 currently costs about $39 per month, but you may need more powerful instances depending on your workload.
We are working on deploying a full stack onto an isolated AWS account and domain name. After this we will be able to measure the baseline costs of the EC2 instances and of other AWS resources, and provide a sample AWS bill.
To the AWS cost you may add a private Github repository[1] (which usually comes for free if you already have a Github account) for the builder-private repository containing credentials; you can alternatively host your own git repository on existing infrastructure. SSL certificates can be obtained for free through Let's Encrypt[2] instead.
[1]
https://github.com/pricing[2]
https://letsencrypt.org/