There are no known pregnancy complications from getting a bikini wax during pregnancy. The skin is unlikely to absorb the wax product used, so there is littlechance of chemical exposure.
Waxing is often associated with pain. Therefore it is suggested that if you are planning to continue waxing through the entire pregnancy, to begin in the early months. This will allow you to, as the pregnancy progresses; build a tolerance for the pain. As the hormone levels increase, the skin may become more sensitive; and waxing may hurt more than before. Also you may experience an increase in hair growth caused by higher hormone levels. Meaning it could be necessary to wax more often.
It is best to test the wax product on a small area that is not noticeable. This would be to make sure there are no adverse reactions. Because the skin could be more sensitive than before becoming pregnant, this would also be used to check for pain tolerance. Also the vessels are more likely to break and become more noticeable. To test in an area that will be inconspicuous is best so you will not feel self-conscious.
If you choose to wax the bikini line, remember that the process could be a bit more uncomfortable than before. Testing to check for reactions and monitoring the hair growth could make for a less painful experience