Mazal tov!

There is no requirement to stop the pill and get a period as preparation for the wedding. You are niddah regardless, and you may continue combining packs as planned. In any case, at this point, it may be too late to start the placebos, wait for withdrawal bleeding to begin and end, and then have enough time to count the seven clean days and immerse before your wedding.

In general, a kallah before her wedding is permitted to perform a hefsek taharah as soon as her bleeding stops, without waiting five days.

You should perform your hefsek taharah a week before your scheduled immersion, which should preferably be as close as possible to the wedding date, no more than four days beforehand. It is recommended to practice doing the hefsek taharah a day or two early rather than wait until the last possible day, in order to familiarize yourself with bedikot, and to have a backup hefsek. Your seven clean days will end on the day of your mikveh immersion.

It is also wise to give yourself the option of extra days on the pill after the wedding, in case it takes a while to consummate the marriage.

Note that this answer applies to your specific situation, where you are certain from long experience that you do not experience breakthrough bleeding when combining packs. For kallot who have begun birth control pills more recently, whose bodies are not yet accustomed to the pills, we would not recommend combining packs of birth control pills immediately before the wedding because of the increased risk of spotting.

Please write back with any follow up questions.

May you merit to build a bayit ne'eman beYisrael!