Vähän is a little as well as bit, even though no one eats a bit of pulla. Flagged
When pulla is baked in the bun form, you generally eat the entire pulla alone, but if the buns are huge (sometimes they are!) you might want to share it/them with someone. However, it's improbable that you'd eat the entire pulla when it's baked in the pitko form (braided loaf). You only eat one, two or more slices of it, when one pullapitko is usually cut into some 20–30 slices. In this sentence, "vähän pullaa" would refer to that or one or two pulla buns.
But that's not what the Finnish sentence means. It means to eat a little bit.