You’ll also need to construct a portfolio of music demos. If there’s one line of work that always requires some sort of example of your skill, it’s songwriting. No publishing company is ever going to hire you if they don’t even know how good you actually are. That said, you need to compose a number of examples of your work to present to whoever you want to hire you.
It’s also important to post your songs online. In this new age of social media and online presence, the more online presence you have, the more a publishing company will think you know what you are doing and already have prior experience. This is important these days because most companies expect you to have some level of online presence to work with. That makes you worth more in their eyes.