It is preferable to wait a few minutes in between attempts at a hefsek taharah. Waiting allows for natural lubrication to return, which can prevent irritation from the bedikah. It also gives a more accurate sense of whether the woman has in fact ceased bleeding. For medical reasons, we usually suggest waiting about ten minutes where possible. But back-to-back attempts are halachically acceptable.
Similarly, a bedikat hefsek taharah may be performed right after washing, internal or external. When a woman cleans herself internally (as is desirable before a hefsek taharah), waiting around ten minutes may be healthier, since it allows time for some of the natural lubrication to return to the area, reducing the chance of irritation to the vaginal lining. Halachically, there may be some preference to wait a few minutes after internal washing, so that new bleeding will show up on the bedikah. But there is no halachic requirement to wait at all between even internal washing and the hefsek taharah.
In contrast, during the seven clean days, we are trying to confirm that a woman has not resumed bleeding. Therefore, washing that is clearly intended to remove blood is more problematic. Once, when daily bathing was not the norm, it was even recommended not to wash oneself at all during the clean days. Nowadays, people generally bathe or shower frequently, and it is acceptable to bathe during the seven clean days as usual. Internal washing is also permissible during the clean days. However, thorough internal washing, such as douching, should be avoided (unless one has a specific ruling for a particular case). We recommend waiting 15-20 minutes after washing before doing a bedikah, both so that it reflects what is really happening, and so as to allow the natural lubricants to return to prevent injury with a dry bedikah. That is a recommendation and not a strict halachic requirement.
Please write back with any further questions.