I don't work in the industry, but I'd take a strong guess and say you'd need an agent to shop around the script for you. If your work is good, start contacting agents and see if one will take you on. I have read that studios have piles of scripts in offices in studio lots and have assistants that just read them all day long. They said most almost all are garbage - not surprising.
Interestingly, I do know that there is a private marketplace website that the major studios use to look at scripts/prices because I saw it in an article/video somewhere. It's not open to the public. I'd guess you'd need an agent to get on that website too.
Good luck!
