That's the thing about the martingale strategy, it doesn't really depend on the amount of your bankroll, but you also should factor in your luck as dice games are one of the common gambling games that depend on it.
Anyway, if you have been really used to playing with the martingale strategy, you should know that you need to set your starting bet much lower than that especially since you only have 100$ to play on. It's pretty common that we can encounter a 5-10 losing streak on dice and you should at least factor that out. I've been using that strategy for quite a while, and I mostly profit from it every time. Patience is a virtue and knowing when to stop are things that you should have when doing the said strategy.
You are right that it doesn't depend on the amount of your bankroll. You can just use the martingale strategy even if you only have $100 bankroll. I would say that the correct term that should be used is that if you want do martingale then you should have decent amount of bankroll to try recover what you have lose. I tried gambling using martingale with just $100 and I did earn profit two times and also lose all $100 when I gambled again.