There are a few different options when it comes to the cheapest bulk E-Mail service. A couple popular ones include Constant Contact and MailChimp. Prices for these services can vary, but they both offer free trials so you can try them out before you commit.
Another option is to go with an email marketing provider like Sendgrid or SparkPost. These providers have a bit higher pricing, but they also offer more features and scalability. If you're expecting a high volume of emails, then one of these providers may be a better option for you.