I guess you mean you've finished writing your proposal?
I think you should email the supervisor telling a bit about yourself, sharing your proposal, and also say that you are very open to their ideas and feedback about the proposal. Also, if you have ideas about funding (e.g., paying for it yourself, applying for x, y, z scheme) then I think it would be important to mention this in the email too.
Even better - if you know someone else who knows the potential supervisor, then you could ask them to introduce you (assuming you are on the same side of the world).
Final tip - if you could have someone in academia read your proposal before sending it to the supervisor, their comments could be helpful.