The next time you shave your legs and notice dryness and bumps after, it could be caused by the irritation you are experiencing from the shaving foam or soap that you are using to aid the shave. If you have sensitive skin, these formulas may be too drying for you. If that's the case, switch to something milder like a gentle facial cleanser or a non-foaming shaving cream. Also, look for razors with more than two blades as they give a closer and smoother shave.
HOT TIP: Hair conditioner makes a good shaving cream!