CI/CD service sending a request to an API hosted within a VPC - time out error

I have an API set up and deployed within a VPC, it's using an internal load balancer.

I have some scripts set up in my CD/CD pipeline (Bitbucket) to send a request to the API Service, for testing purpose. Newman is running a postman collection, but as it's not public facing there's a timeout error, my question here..

What services can I use within AWS, to establish a secure connection from my CI/CD service? I've initially looked into Direct Connect, just wondering if anyone else has come across this issue before. Ideally I don't want to put the APIs public facing, for obvious security reason.

My AWS experience is about 3/4 Months, so looking to build my knowledge up.