One way to prevent the little red bumps is exfoliation. Several hours prior to waxing, you can dry brush your skin to remove dead skin cells and stimulate the glands. However, this should not be done within 6 hours of waxing. Regardless, waxing will typically leave skin looking pink or red for 4-6 hours. Without makeup, there really isn't much to hide the redness.
If you are seeing a professional waxer, please ask questions without hesitation. Most will be happy to answer. If they make you feel uncomfortable, they are probably not the waxer for you. I hope this all worked out for you!