When the mosquito bite, it injects some saliva
to prevent blood clotting while it feeds.
The bump you get after is swollen or itchy, and is a reaction to the injected proteins. This reaction is "allergic" like. The more you are exposed to the mosquito proteins, the more likely for some to have larger, more swollen, and more itchy bumps. These have more allergic component. No bump, no allergy.