Many reasons may be responsible for red bumps but the most common probabilities and precautions to avoid them are:
Closed Pores: Be sure to shave only after soaking the area to be shaved in warm water for three minutes which opens pores. This will also prevent you from having goose bumps, which can produce a red rash if you shave over them.
Exfoliation: Exfoliation is very important, be sure to exfoliate your skin before, after and in between shaving by rubbing with a loofah or wash cloth to avoid bits of skin that may run over by the razor. This will give your skin a smoothness that will allow the razor to glide right over your skin creating no bumps.
Razor: Shaving below the surface of the skin may be the reason. Switch to a single blade razor on areas where these bumps crop up, and shave with the direction of hair growth in these areas.
Toner or Aftershave Lotion: Run over affected areas with toner or with aftershave but do not use these products near the bikini line to disinfect the skin after shaving. Avoid putting lotion on right after you shave because it may clog your pores. Instead, wait an hour or two and then apply a very light, scent-free lotion to combat dryness and to soothe the bumps.
Irritation: Shaving slowly and using plentyof shaving foam can help offset the problem.
Many products are available in the market to remove these bumps, try these products only if someone you trust recommends them. If the little red bumps become really bothersome, consider talking to a dermatologist, who may recommend a product.