I'm a regular visitor (with an account) to a Chinese forum. I see that the internet page claims to have 100,000 users, but I only see 1,000 because it is an ancient Chinese forum. Today I talked to the admin (an old friend of mine; he once asked me to become a moderator) and I said to him, „Sorry for being rude. How did you come up with that 100,000 numbers of members while our forum have less than 1,000 members?“

Is my italicised sentence natural and appropriate?

The „how did you come up with that …“ part of your sentence is fine. What follows is a bit clumsy and doesn't sound natural. Also, what comes before that part, while grammatically correct, could be improved as it won't necessarily be considered rude to raise a polite query in the way you're doing, and at the socio-linguistic level we don't feel the need to apologise in the Anglosphere for asking a question.

So may I suggest:

• I hope this doesn't sound rude, but how did you come up with (the figure of) 100,000 members when our forum has less than 1,000?
• I hope I'm not being rude, but how did you come up with (the figure of) 100,000 members when our forum has less than 1,000?
• I hope you don't mind me asking, but how did you come up with (the figure of) 100,000 members when our forum has less than 1,000?
• I hope I don't come across as (being) rude (here), but how did you come up with (the figure of) 100,000 members when our forum has less than 1,000?

Your version is, of course, perfectly understandable but as you asked if it sounds natural and appropriate, I've offered these suggestions which I hope will help.

Otázky k obhajobě: (…) Ve své práci uvádíte i návratnost vložené investice. Nikde ovšem neuvádíte, jak jste k tomuto číslu přišel. (theses.cz)

In your paper you also state the return on the investment, but nowhere do you explain how you came up with that figure.