Spotting on white underwear does not invalidate the clean days unless it is larger than a gris (roughly, the size of the American dime or Israeli shekel). Some women find that changing their undergarments more frequently helps prevent a larger stain from accumulating. Even a larger stain may not invalidate the clean days depending on its color, and should be brought to a rav for evaluation. Additionally, we advise taking care not to look at toilet paper after using the bathroom. (For more infomation on these topics, please read our articles on staining and toilet paper in the "Becoming Niddah" section of our site.)
For this cycle, you may omit the second bedikah on Thursday, which should mitigate the chances of having a bedikah affected by spotting from the fast. Please be very careful to remember to perform your bedikah in the morning.