Ok, so Gesso basically just adds more “teeth” to the canvas for your paint to stick to. Its not really bumpier in any visible way. But even with untreated canvas you’ll get bleeding if you’re not super careful. Canvas from craft places like Michael’s and Hobby Lobby have often been treated with something that can make it hard to get the paint to stick to the canvas smoothly.
For your application, I would treat the canvas with gesso, then your background color. Let that completely dry. Then attach your stencil and paint the background color again through the stencil. Let it dry without removing the stencil (you can speed this up with a hair dryer or air gun). Then paint your intended stencil color. This makes it so that if the stencil has gaps that would cause bleeding its the background that bleeds into the background color (thus not being really a visible bleed).
This method has made it so that nine times out of ten I get a great stencil. If you do mess up and bleed just remember that you can paint completely over that with your background color and start again.
Ninja Edit: Also, I like to use wax paper or vinyl as a stencil on canvas because it sticks better. With wax paper when you attach it to the canvas you can take a hair dryer or heat gun and melt the wax a bit so that it really sticks to the canvas and then when you’re done you can peel it off. This method isn’t as useful if you want a reusable stencil, though.