I'm not sure why the standard deviation worse case is 5%. Presumably the accuracy of the bot decision plays into it. But I would imagine a couple thousand would get a far more accurate answer.
Now, we want to know the standard error for our estimate of the bot proportion. That is sqrt(p(1-p)/n). Suppose 50% of accounts are bots (I assume that would be very high), then our estimate of p would be 0.5 and our standard error with a sample of 100 would be 0.05. Hence, our 95% confidence interval is roughly 0.4–0.6 in the worst case (with a sample of 100).
If the proportion is under 0.1 (let's assume 0.05), then the standard error would be sqrt(0.05(1-0.05)/100) = 0.022. Our 95% confidence interval in this case would be roughly 0.01–0.09.
These seem like large ranges to me. Hence, I would expect them to use a larger sample too.
For presidential elections it's common to see samples sizes like 1,000 or so, which have standard deviations of around 1.5%. That's better than 5%, and it makes sense since elections are often won by just a few %. But here, IIUC, the goal was to see if bots are a big part of Twitter or not, and so the answer "there are fewer than 5% bots" is enough. That is, we don't care if the % of bots is 3.5% or 4.7%.
What is your 5% value referencing?
https://www.calculator.net/standard-deviation-calculator.htm...
> That has a standard deviation of 0.5 in the very worst case
followed by
> the standard deviation of a random sample scales like 1 over the square root of the sample size, so 0.5 divided by 10 => 0.05 (5%).